(Adds details on conversation between Pelosi and Mnuchin)
By Susan Cornwell and David Morgan
WASHINGTON, Sept 16 (Reuters) - President Donald Trump urged his fellow Republicans on Wednesday to go for "much higher numbers" in a coronavirus aid bill, as Washington remained deadlocked over economic relief from the crisis ahead of the Nov. 3 elections.
Senate Republican reaction to Trump's appeal was mixed, but generally cautious. But House of Representatives Speaker Nancy Pelosi and Senate Democratic leader Chuck Schumer said in a joint statement they were encouraged and hoped White House negotiators would now "meet us halfway."
Pelosi spoke by phone on Wednesday to Treasury Secretary Steven Mnuchin, who has helped negotiate previous coronavirus aid packages. They talked about a government funding bill, and at the end of the conversation, Pelosi reiterated the points she had made in her statement with Schumer, Pelosi's spokesman said on Twitter.
The standoff dates to mid-May, when the Democratic-majority House approved $3.4 trillion in new coronavirus aid, including unemployment benefits, money for schools, the U.S. Postal Service, and testing. Pelosi meanwhile offered to drop the demand to about $2.2 trillion.
The Senate's Republican leaders countered with a $1 trillion plan, but some of their own members balked at that. Last week they put a $300 billion bill up for a vote that Democrats blocked as insufficient.
"Go for the much higher numbers, Republicans, it all comes back to the USA anyway (one way or another!)" Trump wrote on Twitter Wednesday.
Congress and the White House approved more than $3 trillion worth of coronavirus relief measures earlier this year.
The Senate's number two Republican John Thune, speaking after Trump's tweet, said proposals should stay in a "realistic" range. Noting the original $1 trillion Senate Republican plan, he said: "As you go upwards from there you start ... losing Republican support pretty quickly."
A $1.5 trillion compromise floated Tuesday by the House Problem Solvers Caucus, a bipartisan centrist group, was attacked by members of both parties. White House Chief of Staff Mark Meadows, however, said it deserved consideration.
The approaching election increases the political stakes for both parties. Pelosi faces growing pressure from moderate House Democrats for more action on COVID-19 relief. Some of them welcomed Trump's tweet on Wednesday, including Representative Max Rose, from a competitive congressional district in Staten Island, New York.
Rose said leaders of both parties should "Stop the game, stop the stupidity and get to work" on a coronavirus aid plan.
Thune said there was some Republican interest in the $1.5 trillion Problem Solvers plan, but not in the $500 billion it included in aid for state and local governments. Meadows said the state and local issue was probably the biggest obstacle to a deal.
Several Senate Republicans said their recent $300 billion offer was about the right amount, signaling doubt they could go higher.
"So the president has his opinion, we have ours," Senator Ron Johnson said.
(Reporting by Susan Cornwell and David Morgan; additional reporting by Alexandra Alper; editing by Jonathan Oatis and Timothy Gardner)