Across the olive groves and wheat fields of the northern Syrian province of Aleppo, a battle with global dimensions risks erupting into a wider war.

Russian warplanes are bombing from the sky. Iraqi and Lebanese militias aided by Iranian advisers are advancing on the ground.

An assortment of Syrian rebels backed by the United States, Turkey, Saudi Arabia and Qatar are fighting to hold them back. Kurdish forces allied both to Washington and Moscow are taking advantage of the chaos to extend Kurdish territories. The DAISH has snatched a couple of small villages, while all the focus was on the other groups.

Ahead of a supposed pause in the hostilities negotiated by world powers and due to be implemented later in the week, the conflict seems only to be escalating.

Turkey joined in over the weekend, firing artillery across its border at Kurdish positions for a second day Sunday and prompting appeals from the Obama administration to both Turks and Kurds to back down.

Syria's civil war long ago mutated into a proxy conflict, with competing world powers backing the rival Syrian factions almost since the earliest days of the armed rebellion against President Bashar al-Assad.

But perhaps never before have the dangers - or the complications - of what amounts to a mini world war been so apparent as in the battle underway for control of Aleppo.

Russian Prime Minister Dmitri Medvedev warned of the risks at a security conference in Munich on Saturday, saying that the world had already descended into "a new Cold War."

"There's a spiral of insecurity here that is not being managed," said Salman Shaikh, a political consultant whose Shaikh Group is engaged in mediation efforts in the Syrian war. "What we are seeing is a classic, really complicated balance-of-power struggle that could become a very dangerous situation."

For now, the focus of the fighting is the rural hinterland of Aleppo, a landscape of rolling farmland dotted with villages and towns that are steadily being pulverized by the relentless Russian bombardments.

Residents said the intensity of the strikes has increased since the announcement of the cease-fire agreement, perhaps as Russia and its allies seek to maximize their gains ahead of its possible implementation.

Defeating the rebels here would enable the government to encircle and eventually crush the rebels in their stronghold in the eastern portion of the city of Aleppo, perhaps inflicting a decisive blow to the five-year-old rebellion against Assad's rule.

But more is at stake than the outcome of Syria's war. The Aleppo offensive is affirming Moscow's stature as a dominant regional power across the heart of the Middle East.

The advances by Shiite Iraqi and Lebanese militias are extending the sway of Iran far beyond the traditional Shiite axis of influence into Sunni areas of northern Syria.

Although Syria's army is claiming the victories, rebels, military experts and videos by the fighters themselves say almost all of the advances are being made by the Lebanese Hezbollah movement, the Iraqi Badr Brigade, Harakat al-Nujaba and other Iraqi Shiite militias that are sponsored by Iran.

Meanwhile, the Aleppo countryside is emptying. Tens of thousands of people have streamed north to the Turkish border to escape the airstrikes, where they are being blocked by a Turkish government that is hosting 2.5 million Syrian refugees.

They tell stories of entire villages being crushed and communities displaced. Mohammed Najjar, a resident of the town of Marae at the heart of the contested rural area, said that barely 5 percent of the town remained behind.

His extended family had lost 15 houses just since the Aleppo offensive began two weeks ago, he said, speaking by telephone from the border area after he fled Marae last week.

Emile Hokayem of the International Institute for Strategic Studies said that driving people out of their homes has long been part of the Syrian government's strategy.

"They're depopulating areas of people whose loyalties are impossible to recover," he said. "It's a much cheaper and easier way to occupy territory than by trying to win hearts and minds. They're simply going to push people out so that there is no insurgency."

For Turkey, the biggest concern is that the vacuum along its borders will be filled by Kurds, whose dreams of independence have been brought closer by the chaos in Syria.

The People's Protection Units, or YPG, have already been taking advantage of U.S. airstrikes in eastern Syria to expand a Kurdish enclave there. Now they are taking advantage of the Russian airstrikes around Aleppo to extend eastward from Afrin, another Kurdish enclave.

The stated Kurdish goal is to link the two enclaves into one extended Kurdish territory that would span more than half of Turkey's border with Syria.

The Kurdish expansion has caused friction between Washington and Ankara because Turkey regards the YPG as an affiliate of the Turkish Kurdish organization known as the PKK, which is designated as a terrorist organization by the United States and Turkey. But the United States does not regard the YPG as a terrorist group and has worked closely alongside it in the fight against the DAISH.

Now, fighters with an alliance of Kurds and Arabs led by the YPG are closing in on the border town of Azaz, which controls the biggest Turkish gateway into Syria.

Turkish artillery opened fire Saturday and again Sunday against two villages and an air base recently captured by the advancing Kurds - in retaliation, a Turkish military statement said, for shells fired by the YPG that landed on a military base inside Turkey.

Vice President Biden telephoned Turkish Prime Minister Ahmet Davutoglu on Saturday to urge Turkey to halt its shelling. He emphasized "the imperative for de-escalation in the area," according to a White House statement Sunday.

Separately, a State Department statement called on the Kurds "not to take advantage of a confused situation by seizing new territory."

Within hours of the appeals, the Kurds seized another northern Aleppo village, Ain Daqna, and Turkey resumed its bombardment.

There is no mood in Turkey for a war in Syria, but the risk of an unintended escalation is real, said Faysal Itani of the Washington-based Atlantic Council. Tensions between Russia and NATO member Turkey are already sky-high following Turkey's downing of a Russian jet last November, and any miscalculation could quickly trigger a Russian response.

"Turkey is under immense pressure," he said. "It has a quasi-Kurdish state emerging on its border, and the groups it championed are being destroyed."

Saudi Arabia also has talked of sending troops to Syria, prompting some speculation that the kingdom may be preparing to support a Turkish incursion. Foreign Minister Adel al-Jubeir said Sunday, however, that Riyadh would send special forces only if the United States decides ground forces are needed for the fight against the DAISH. "So the timing is not up to us," he said during a news conference in Riyadh.