WASHINGTON - US Senate Democrats on Tuesday rejected a Republican proposal to fund the Department of Homeland Security (DHS), a plan supported by President Donald Trump, as the DHS shutdown stretches into its second month.

The proposal would fund almost all DHS but set aside some funding for Immigration and Customs Enforcement (ICE), in an attempt to end the department's shutdown, which has resulted in staffing shortages for Transportation Security Administration (TSA) workers at some airports.

At a press conference, Senate Minority Leader Chuck Schumer told reporters that Democrats will present a counteroffer to Republicans, insisting on reforms to rein in ICE.

The fatal shootings of two US citizens -- Renee Good and Alex Pretti -- by federal enforcement in Minneapolis in January have prompted Democrats to seek changes to how immigration agencies operate.

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Over the past few weeks, negotiations between the two parties on immigration enforcement have shown little progress.

The Senate on Friday rejected the DHS funding bill for the fifth time, leaving key operations -- including the TSA, the Coast Guard and the Federal Emergency Management Agency -- severely strained.