Speaking to reporters at the White House, Trump said Ukraine was getting hit very hard by Russia and needed to be able to defend itself. The United States would be sending primarily defensive weapons, he said.
Trump on Friday told reporters Ukraine would need Patriot missiles to defend itself, but did not mention them again specifically on Monday.
"We're going to send some more weapons. We have to. They have to be able to defend themselves. They're getting hit very hard, now. They're getting hit very hard. We're going to have to send more weapons, defensive weapons, primarily," he said at the start of a dinner with Israeli Prime Minister Benjamin Netanyahu.
After a call with Trump on Friday, Ukrainian President Volodymyr Zelenskiy said he had agreed to work on increasing Kyiv's capability to "defend the sky" as Russian attacks escalated. He said he discussed joint defence production, purchases and investments with Trump.
Ukraine has been asking Washington to sell it more Patriot missiles and systems that it sees as key to defending its cities from intensifying Russian air strikes.
A decision by Washington to halt some shipments of weapons to Ukraine prompted warnings by Kyiv the move would weaken its ability to defend against Russia's air strikes and battlefield advances. Germany said it is in talks on buying Patriot air defence systems for Ukraine to bridge the gap.
The US president's comments come after Russia struck two military recruitment centres in separate drone attacks, doubling down on a new campaign of strikes that Kyiv says is aimed at disrupting military recruitment.
Monday's attacks damaged draft offices in the regional capitals of Kharkiv and Zaporizhzhia and came a day after a Russian drone struck a recruitment centre in the central Ukrainian city of Kremenchuk.
Last week, Russian attacks targeted draft offices in Poltava, another regional capital, as well as President Volodymyr Zelenskiy's hometown of Kryvyi Rih.
Both strikes on Monday took place in densely populated areas, wounding dozens of civilians and damaging homes and apartment buildings.
In Kharkiv, rescue workers sifted through debris as stunned residents recovered.
"This is the tactic our enemy has chosen," Mayor Ihor Terekhov told reporters in front of a badly charred building.
In its daily briefing on Monday, Russia's defence ministry confirmed it had struck an unspecified number of draft offices.
The string of attacks has prompted recruitment centres to disperse some personnel and temporarily suspend work at the locations damaged, ground forces spokesperson Vitaliy Sarantsev told Ukrainian public broadcaster Suspilne.
However, he added that recruitment was still on track.
Ukraine's resource-strapped military has struggled to fend off a bigger and better-equipped Russian army on the battlefield, where Moscow has made gradual advances across parts of the east in a grinding summer campaign.
Enthusiasm for joining up in Ukraine has also been dampened by reports of corruption, as well as poor training and command.
Ukraine's National Security and Defence Council warned on Monday that Russia was also waging an "information campaign" by spreading a bot on messaging platform Telegram that purports to collect information about the location of draft offices.
"This ... indicates a coordinated attempt by Russia to destabilise the mobilisation process and sow panic among the population," the Centre for Countering Disinformation said in a statement.
The recent strikes also follow a string of bombings at recruitment centres and arson attacks on military vehicles earlier this year, which Ukraine's domestic security service has said is Russian sabotage.
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