WASHINGTON (Reuters) - U.S. Senate Republicans aim to vote this week on their own plan to advance President Donald Trump's agenda on border security, immigration, fossil fuel production and defense, pushing ahead of a rival Republican blueprint in the House of Representatives.

Senate Republicans pushed ahead late on Tuesday on a scaled-back budget bill, a USD 340 billion package to give the Trump administration money for mass deportations and other priorities, as Democrats prepare a counter-campaign against the onslaught of actions coming from the White House.

The Republican-led U.S. Senate, in a bid to overcome party infighting over President Donald Trump's agenda, will begin moving forward as early as next week on a $300 billion, four-year plan to fund his border security and military priorities.

The Senate maneuvered past a procedural hurdle on its preferred Trump budget bill after leapfrogging the House Republicans, who were expected to take the lead on the process.

Senate Republicans are set to vote on their budget resolution this week as the chamber makes its move toward enacting a big chunk of President Trump’s agenda. Senate Majority Leader John Thune (R-S.D.

The Senate took its first procedural step Tuesday on a budget blueprint that would pave the way for a filibuster-proof border security, defense and energy package, a key part of President Donald Trump’s legislative agenda.