He called Pelosi's trip a "public relations event".
"Once again, we call upon the president to reopen government", Pelosi said.
The partial shutdown - the longest in US history - is in its fourth week. It added that the department's leadership was "deeply concerned" about the financial hardships its employees are facing.
"There is definitely a sense that there is a deadline approaching, which would be next Tuesday, to make sure that we're able to solve this problem", said Mercedes Schlapp, a White House spokeswoman.
The House and Senate had previously voted overwhelmingly in favor of the act.
Of all the issues at stake as President Donald Trump and Democrats wrangle over his prized border wall, the latest snag is whether bargaining over the proposal should come before or after shuttered government agencies reopen.
Secretary of State Mike Pompeo had raised eyebrows among the USA diplomatic corps last week when he proclaimed that morale at the State Department was "good" despite the shutdown and the fact that 40 percent of its employees in the US and almost 23 percent overseas had been furloughed and the rest were working without pay.
President Donald Trump began insisting on $5 billion for a border wall between the USA and Mexico at the end of November after submitting a budget that contained $1.6 billion for border security, including parts of the wall.
He also said the house speaker's party becomes more of a political loser as the president continues to shine a spotlight on the human tragedies from its open border policies.
They had been warned off such a strategy by Vice President Mike Pence and White House senior adviser Jared Kushner, who told them Trump opposed such a short-term fix, but the senators pressed on anyway, trying to get 20 Democrats and 20 Republicans to join.
Pelosi is refusing money for the wall, which she views as ineffective and immoral.
Democrats will object that the Gang of Eight bill did fund a border wall, but it was in exchange for a lot of concessions. "First things first: we must reopen the government".
The shutdown, now in its 26th day, affects nine government departments, including the Department of Homeland Security, of which the Secret Service is a component.
Altogether, 38 percent said they met at least one of those conditions. Mr. Trump said Pelosi could still use commercial transportation for the trip.
Wisconsin Republican senator Ron Johnson said the matter was less about security than about Ms Pelosi feeling she had the upper hand in the budget standoff.
The shutdown is dragging on due to an entrenched stalemate between Trump and congressional Democratic leaders over funding for the president's proposed border wall. Maybe he thinks it's OK not to pay people who do work. Typically, fewer than 1,000 former federal employees apply for jobless benefits each week. But those who are working without pay are not.
The current shutdown, which tallies now at a listless 27 days, broke the record for longest shutdown in American history. "Because if you do it now, they'll shut down the government next year for something else.' I share that sentiment".
The Transportation Security Administration says 6.1 percent of its airport screeners missed work Wednesday. Call-outs peaked on Sunday at 7.7 percent compared to 3.2 percent the same day previous year.
The National Archives are closed because of the government shutdown.
Wildfire training courses are being canceled, piles of dead trees are left untended in federal forests and controlled burns to thin fire-prone forests aren't happening. Also, about 340,000 workers have been furloughed.
The shutdown is in its fourth week. An estimated 800,000 federal workers have been adversely affected by the lapse in funding.
The White House had no immediate comment on Pelosi's request.
The US Constitution requires the President to brief Congress on the state of the union, but that briefing is not required to be a speech in front of Congress. President George Washington and his successor, John Adams, both delivered their annual messages as speeches before Congress. President Thomas Jefferson began the practice of delivering the State of the Union in writing. "People in the White House don't like hearing that".
President Trump's economists have now doubled projections of how much economic growth is being lost each week.