WASHINGTON—Congressional leaders were on the cusp of striking a two-year budget deal Tuesday to boost federal spending levels for both the military and domestic programs, after separating for now a stalled immigration fight from efforts to keep the government funded.

The emerging agreement is expected to increase military spending by $80 billion a year and nondefense spending by $63 billion a year, according to lawmakers and congressional aides, though the numbers were still being negotiated.

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