"I don't think a government shutdown is necessary and I don't think most people want to see a government shutdown, ourselves included," the leader of the Republican-controlled House said at a news conference in Oregon where he was promoting tax reform.
Ryan argued the House had already passed funding for border security but that the narrowly divided Senate -- where Democrats have considerably more sway over what gets into funding bills -- would need more time to act.
"The fact is though, given the time of year it is and the rest of the appropriations we have to do, we are going to need more time to complete appropriations process particularly in the Senate," Ryan said.
Ryan also said a short-term government funding bill, known as a continuing resolution, would probably be needed to keep the government open past September.
At a raucous rally in Phoenix Tuesday night, Trump said he would insist on the border wall funding.
"If we have to close down our government, we're building that wall," Trump said.
Senate Minority Leader Chuck Schumer also warned against a shutdown over the border security issue.
"If the President pursues this path, against the wishes of both Republicans and Democrats, as well as the majority of the American people, he will be heading towards a government shutdown which nobody will like and which won't accomplish anything," the New York Democrat said in a statement.
In the current politically polarized environment -- when Trump is battling Republicans on the Hill
as hard as he is Democrats -- it's highly uncertain if a government shutdown can be avoided. But GOP leaders on the Hill have made clear their desire to avoid the potentially politically damaging outcome.
Ryan was asked about Trump's harsh criticism of Arizona's two GOP senators, John McCain and Jeff Flake.
"I would just say that I think it's important that we all stay unified as Republicans to complete our agenda," Ryan said. "Those two gentlemen are people I respect, know, like and are friends with -- and we disagree on certain issues. I can think of a couple with those gentleman, but nevertheless we have very good working relationship. I think it's important we stay unified but I think the President is employing a strategy he thinks is effective for him."