Story highlights Congress rejected a request for more wall money earlier this year

The budget would also fund border technology and immigration enforcement hiring

Washington (CNN) President Donald Trump's 2018 budget calls for more spending for border security and immigration enforcement -- but the ask is still modest compared to what fulfilling his campaign pledges would likely cost.

The budget proposed by the White House on Tuesday includes $2.6 billion for border security -- $1.6 billion of which will be for "bricks and mortar for a wall," Office of Management and Budget Director Mick Mulvaney told reporters on Monday.

A source familiar with the budget justification says the money would largely cover just a few dozen miles of wall, tracking what the administration had previously proposed for the $1 billion it asked for unsuccessfully for 2017 construction.

As CNN previously reported , that $1 billion was requested for just 62 miles of border barrier, 14 of which was replacement fencing.

Estimates for funding a full wall across the entire Southern border have ranged in the tens of billions of dollars. Despite Trump's repeated pledges to immediately begin on such a wall, his Department of Homeland Security has made clear that it would consider a variety of border barrier options and would not seek to build them "from sea to shining sea," as Secretary John Kelly told Congress last month.

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