U.S. President Donald Trump accused predecessor Barack Obama on Saturday of wiretapping him during the late stages of the 2016 election campaign, but offered no evidence for an allegation which an Obama spokesman said was "simply false".

Trump made the accusation in a series of early morning tweets just weeks into his administration and amid rising scrutiny of his campaign's ties to Russia.

"How low has President Obama gone to tapp my phones during the very sacred election process. This is Nixon/Watergate. Bad (or sick) guy!," Trump wrote in one tweet. "I'd bet a good lawyer could make a great case out of the fact that President Obama was tapping my phones in October, just prior to Election!"

The remarkable tussle between the current and former presidents just 45 days since the handover of power is the latest twist in a controversy over ties between Trump associates and Russia that has dogged the early days of his presidency.

U.S. intelligence agencies concluded last year that Russia hacked and leaked Democratic emails during the election campaign as part of an effort to tilt the vote in Trump's favor. The Kremlin has denied the allegations.

Trump has accused officials in Obama's administration of trying to discredit him with questions about Russia contacts.

READ: Trump says Obama wiretapped him during campaign; gives no evidence

Obama spokesman Kevin Lewis said it had been a "cardinal rule" of the Obama administration that no White House official ever interfered with any independent investigation led by the Department of Justice.

"Neither President Obama nor any White House official ever ordered surveillance on any U.S. citizen. Any suggestion otherwise is simply false," Lewis said in a statement.

The statement did not address the possibility that a wiretap of the Trump campaign could have been ordered by Justice Department officials.

Trump said the alleged wiretapping took place in his Trump Tower office and apartment building in New York, but there was "nothing found." The White House did not respond to a request to elaborate on Trump's accusations.

AIDES CAUGHT BY SURPRISE

Trump was spending the weekend at his Florida seaside resort, Mar-a-Lago. He was scheduled to meet with Attorney General Jeff Sessions and Homeland Security Secretary John Kelly before a dinner with officials also including adviser Steve Bannon and White House Counsel Don McGahn, the White House said.

Amid a political storm, Sessions on Thursday announced he would stay out of any probe into alleged Russian meddling in the 2016 presidential election after it emerged he met last year with Russia's ambassador, although he maintained he did nothing wrong by failing to disclose the meeting.

A Trump spokeswoman said the president spent part of Saturday "having meetings, making phone calls and hitting balls" at his golf course in West Palm Beach.

His supporters, meanwhile, staged small rallies in at least 28 of the country's 50 states, most of which passed off peacefully. But there were clashes in the famously left-leaning city of Berkeley, California, where protesters from both sides hit each other over the head with wooden sticks.

Trump's tweets caught his aides by surprise, with one saying it was unclear what the president was referring to.

Members of Congress said Trump's accusations require investigation or explanation.

Senator Ben Sasse, a Republican, described the allegations as serious and said the public deserved more information. He said in a statement it was possible that Trump had been illegally tapped, but, if so, the president should explain what sort of tap it was and how he knew about it.

U.S. Representative Adam Schiff, the top Democrat on the House Intelligence Committee, called Trump's assertion a "spectacularly reckless allegation".

"If there is something bad or sick going on, it is the willingness of the nation's chief executive to make the most outlandish and destructive claims without providing a scintilla of evidence to support them," Schiff said in a statement.

Former Obama adviser Ben Rhodes strongly denied Trump's allegations: "No president can order a wiretap. Those restrictions were put in place to protect citizens from people like you," Rhodes wrote on Twitter.

RUSSIA SANCTIONS

Trump's administration has come under pressure from Federal Bureau of Investigation and congressional investigations into contacts between some members of his campaign team and Russian officials during his campaign.

Republican Senator Lindsey Graham said he had no knowledge of any wiretapping but was "very worried" about the suggestion Obama had acted illegally and would also be concerned "if in fact the Obama administration was able to obtain a warrant lawfully about Trump campaign activity."

Several other Republicans again urged an investigation into a series of intelligence-related leaks.

Obama imposed sanctions on Russia and ordered Russian diplomats to leave the United States in December over the country's involvement in hacking political parties in the Nov. 8 U.S. presidential election.

Under U.S. law, a federal court would have to have found probable cause that the target of the surveillance is an "agent of a foreign power" in order to approve a warrant authorizing electronic surveillance of Trump Tower.

Several conservative news outlets and commentators have made allegations in recent days about Trump being wiretapped during the campaign, without offering any evidence.

Trump's first national security adviser, Michael Flynn, resigned in February after revelations that he had discussed U.S. sanctions on Russia with the Russian ambassador to the United States before Trump took office.

Flynn had promised Vice President Mike Pence he had not discussed U.S. sanctions with the Russians, but transcripts of intercepted communications, described by U.S. officials, showed that the subject had come up in conversations between him and the Russian ambassador.