PITTSBURGH — Still reeling from the horror and grief after Saturday’s massacre at the Tree of Life synagogue, Pittsburgh is now dealing with something else: the barbed politics of the 2018 midterms and widespread opposition to President Trump’s plan to visit here Tuesday.

Jewish leaders said that President Trump was not welcome in Pittsburgh and accused him of stirring up extremism.

Mayor William Peduto, who strongly rejected Mr. Trump’s suggestion that armed guards in houses of worship are the answer to violence, warned that the president would be a distraction from funerals taking place Tuesday.

Many in the Jewish community in Pittsburgh cited what they saw as the president’s divisive rhetoric, which they feel had a role in enabling the violence here, as well as other recent episodes including the mail bombs sent from Florida to prominent Democratic figures and what appears to be the racial killing of two black shoppers near Louisville, Ky. Interviews in Florida reflected a similar urgency and unease about the intersection of violence in American life and the looming midterm elections.

The incidents returned to a boil a long-running issue dating at least to the white nationalist rally in Charlottesville, Va., in 2017, when Mr. Trump was widely condemned for equating neo-Nazis with demonstrators protesting them.

Now, one week before Americans head to the polls, criticisms that the president is sowing hurtful divisions in society have become an electoral issue, a turn of events that the White House and Republicans are vehemently pushing back on. Chants of “Vote! Vote! Vote!” broke out during vigils for victims of the synagogue shootings.

The U.S. military said it would send 5,200 troops to the southwest border in response to a caravan of migrants from Central America that President Trump has seized on as an issue in the Nov. 6 midterm elections.

The movement is the largest, quick deployment of active-duty U.S. troops since the response to the 2010 earthquake in Haiti, when thousands arrived within days, former officials said. It is a major escalation of the U.S. response at the border, which as recently as last week was planned for 800 troops. With 2,000 National Guard members already in place, it will exceed the combined U.S. military footprint in Iraq and Syria.

“Our first level of effort will be to harden the points of entry and address key gaps in areas around the points of entry,” said Air Force Gen. Terrence J. O’Shaughnessy, commander of the U.S. Northern Command, which is responsible for the continental U.S.

With the balance of power in Congress up for grabs next Tuesday, President Trump has seized on the migrant caravan to rally his Republican supporters. Close U.S. Senate or House elections are being fought in the border states of Arizona, California and Texas.

“This is an invasion of our Country and our Military is waiting for you!” Mr. Trump wrote Monday morning on Twitter, without directly mentioning troop numbers.

Critics of the president said the use of active-duty troops is a political gambit and that the domestic deployment will degrade military readiness for defense abroad.

“When Donald Trump deploys troops for a nonexistent threat, that means troops are not training or preparing for the fights that could be on the horizon, for legitimate threats,” said Will Fischer, director of government relations for VoteVets, a pro-Democratic advocacy group. “This is a campaign ploy.”