WASHINGTON — The House today passed and sent to President Barack Obama a far-reaching extension of the Violence Against Women Act.

The vote came after House Republican leaders, cognizant of divisions in their own ranks and the need to improve their faltering image among women voters, accepted a bill that cleared the Senate two weeks ago on a strong bipartisan vote.

The bill renews a 1994 law that has set the standard for how to protect women, and some men, from domestic abuse and prosecute abusers. Today’s 286-138 vote came after House lawmakers rejected a more limited approach offered by Republicans.

It was the third time this year that House Speaker John Boehner has allowed Democrats and moderates in his own party prevail over the GOP’s much larger conservative wing.

As with a Jan. 1 vote to avoid the fiscal cliff and legislation to extend Superstorm Sandy aid, a majority of House Republicans voted against the final anti-violence bill.

The law has been renewed twice before without controversy, but it lapsed in 2011 as it was caught up in the partisan battles that now divide Congress.