Wall Street experienced another volatile session, boosted by reports of progress in the US-China trade war, but buffeted by President Donald Trump's threat to shut down the government over border security funding.

Major US indices ended little changed.

Britain's prime minister met with German Chancellor Angela Merkel in an effort to win concessions from European leaders after postponing a parliamentary vote on the plan.

Merkel told lawmakers of her CDU/CSU bloc she saw "no way to change" the agreement, according to sources at the party meeting.

The British pound continued to retreat, falling to $1.2481, a decline of nearly two percent from last week.

"A strong sense of uncertainty over the various scenarios that could happen regarding Brexit is likely to leave investors extremely uneasy and edgy," said Lukman Otunuga, an analyst at FXTM.

"As the week progresses market players will be pondering whether May has the ability to renegotiate with Brussels in a bid to save the deal? If she will face a leadership vote or the possibility of a second referendum."

But London's FTSE 100 added 1.3 percent and Frankfurt closed 1.5 percent higher.

Paris rose by nearly as much after President Emmanuel Macron made spending promises worth up to 11 billion euros ($12.5 billion) aimed at quelling the "yellow vest" unrest.

While the news pushed French government bond yields higher and helped depress the euro, the Paris bourse was more focused on the potential impact of the measures on growth, analysts said.

"As long as he (Macron) continues with pro-growth supply-side reforms, the French economy can strengthen over time despite a cyclical slowdown now," said Kallum Pickering, senior economist at Berenberg.

France faced more turmoil late Tuesday with a shooting in Strasbourg that killed at least two people and seriously injured another 11.

- Shutdown threat -

Back in the US, investors cheered talks between Beijing and Washington to set up a timetable and agenda for trade talks, and reports China agreed to cut tariffs on US autos to 15 percent from 40 percent.

But stocks were pressured by Trump's contentious White House meeting with congressional Democratic leaders who refused to support his demand for $5 billion to build a wall between Mexico and the United States.

"If we don't get what we want one way or the other ...I will shut down the government," an incensed Trump told Democratic leaders Nancy Pelosi and Chuck Schumer. "I am proud to shut down the government for border security."

Karl Haeling of LBBW said government shutdowns had not historically had a major impact on the US stock market.

"It certainly did not inspire any confidence that the people who are the top leaders of our country could engage in such in such childish behavior," Haeling said.

He said there was still hope US stocks could rally into the end of the year but there were "a lot of underlying concerns" among investors