WASHINGTON — Washington negotiations on a huge COVID-19 relief bill took a modest step forward on Tuesday, though time is running out and Senate Majority Leader Mitch McConnell, President Donald Trump’s most powerful Senate ally, is pressing the White House against going forward.

McConnell on Tuesday told fellow Republicans that he has warned the White House not to divide Republicans by sealing a lopsided $2 trillion relief deal with House Speaker Nancy Pelosi before the election — even as he publicly said he’d slate any such agreement for a vote.

Pelosi’s office said talks with Treasury Secretary Steven Mnuchin on Tuesday were productive, but other veteran lawmakers said there is still too much work to do and not enough time to do it to enact a relief bill by Election Day.

McConnell made his remarks during a private lunch with fellow Republicans on Tuesday, three people familiar with them said, requesting anonymity because the session was private.

The Kentucky Republican appears worried that an agreement between Pelosi and Mnuchin would drive a wedge between Republicans, forcing them to choose whether to support a Pelosi-blessed deal with Trump that would violate conservative positions they’ve stuck with for months. Many Republicans say they can’t vote for another huge Pelosi-brokered agreement.

McConnell said if such a bill passed the Democratic-controlled House with Trump’s blessing “we would put it on the floor of the Senate.” Those public remarks came after the private session with fellow Republicans.

Trump is hoping for an agreement before the election, eager to announce another round of $1,200 direct payments going out under his name, but it’s increasingly clear that time has pretty much run out. If he wins, Trump is promising relief, but if he loses — as polls are indicating — it’s unclear that his enthusiasm for delivering COVID aid will be as strong. Recent history suggests that any post-election lame-duck session in the event of a Trump loss wouldn’t produce much.