Washington (CNN) After a deadly terrorist attack in New York City, critics of President Donald Trump on Wednesday pointed to the millions in proposed cuts to counterterror programs sought by his administration, which reduced multiple such initiatives in its budget request.

The Trump administration has proposed sharp cuts to programs that seek to prevent domestic terrorism and prepare localities to respond -- a point made by Senate Minority Leader Chuck Schumer, a Democrat from New York, in response to Trump criticizing him on Wednesday morning, in a tweet linking the attack to an immigration policy Trump ascribed to Schumer.

"President Trump, instead of politicizing and dividing America, which he always seems to do at times of national tragedy, should be focusing on the real solution - anti-terrorism funding - which he proposed cutting in his most recent budget," Schumer said in a statement. "I'm calling on the President to immediately rescind his proposed cuts to this vital anti-terrorism funding."

The Department of Homeland Security says, for its part, that it continues to improve the administration's efforts on countering terrorism, and promises more effective measures to come.

Trump's 2018 budget proposal included steep cuts to a number of grant programs run by the Department of Homeland Security that go toward terrorism and violent extremism preparedness and prevention. All told, more than $300 million would be cut from such programs.

New York itself would stand to lose millions in federal funds. On Tuesday, a 29-year-old Uzbek national killed eight people and injured more than a dozen more when he drove a rented truck onto a bike and pedestrian path in Manhattan, pledging his support to ISIS in a note found at the scene.

The administration has also folded two counterterror grant programs altogether, and is in the process of rebranding the Obama administration's Countering Violent Extremism office.

A senior DHS official earlier this fall disputed the notion that the administration was retreating from fighting terrorism and domestic extremism, though, saying a new strategy is forthcoming.

"We really intend to elevate and amplify our terrorism prevention efforts in a big way, because the threat environment is serious, we're taking it seriously and we're doing a full end-to-end review of what we do on terrorism prevention to make sure that our efforts are effective," the official told CNN. "We do not intend to focus our terrorism prevention efforts exclusively on one ideology. DHS is committed to combating both domestic terrorism and international terrorism and bolstering efforts for both."

Millions in cuts

Two grant programs -- Countering Violent Extremism and Complex Coordinated Terrorist Attacks -- would be eliminated entirely from the Federal Emergency Management Agency's budget under Trump's plan, to the tune of nearly $49 million. The budget also would cut two full-time employees managing the program.

Congress has also declined to reallocate money for the Countering Violent Extremism program in its proposed budgets, though it cited the slowness in disbursing funds it appropriated previously as a reason.

A DHS official said the intent of the program was always experimental and its results still needed to be assessed. The administration sees the money as "testbed funding to assess counterrecruitment and counterradicalization efforts nationwide to determine what efforts are effective -- and what efforts are not," the official said.

The administration's budget documents say the program goals can be achieved through other grants, like the State Homeland Security Program, but those would also be slashed in Trump's budget.

Overall, the DHS grant program's budgets cut by more than $200 million. The State Homeland Security Program budget would be cut by $117 million, and the Urban Area Security Initiative, also cited by FEMA as a replacement for the pair of grant programs, would be cut by $150 million.

Similarly, the Emergency Management Performance Grant Program would be cut by $70 million.

A program run by the Transportation Security Administration, called the Visible Intermodal Prevention and Response program, would also be drastically cut. Such teams support security efforts on all modes of transportation, and also deploy for security of major events like sports' championship games and Inauguration. Those would be cut from 31 teams to eight, totaling $43 million.

New York City and the state, for example, could millions of dollars under the grant cuts.

The New York State Division of Homeland Security and Emergency Services got nearly $1.4 million in fiscal year 2016 from the Complex Coordinated Terrorist Attacks, which the Trump administration would cut entirely, according to award notice documents.

Under the 2017 allocation, New York got nearly $77 million from the State Homeland Security Program and $15 million from the Emergency Management Performance Grant program, according to DHS allocation documents obtained by CNN. The New York City area also got $178 million from the Urban Area Security Initiative. All of those programs would be decreased by roughly 20% to 25% across the board under the 2018 budget proposal.

In testimony before Congress earlier this year, acting Secretary Elaine Duke told lawmakers that administration is evaluating its approach to preventing terrorism going forward -- and she and other officials have begun calling it "terrorism prevention" instead of "countering violent extremism."

"Americans do not want us to simply stop violent plots, they want us to keep them from materializing in the first place," Duke said in her prepared testimony. "As part of this effort, we have launched an end-to-end review of all DHS 'countering violent extremism' or CVE programs."

Nevertheless, DHS officials have faced numerous questions from lawmakers about the proposed cuts to the programs and criticism from counterterror experts. The House-passed 2018 budget, which still needs to pass the Senate, largely increases or maintains the funding that Trump has proposed to cut.