WASHINGTON — Vice President Mike Pence cast the tiebreaking votes in the Senate on Thursday on a measure that would enable states to strip some federal funds from women’s reproductive-health organization Planned Parenthood and other health-care providers.

With Pence’s vote, the Senate voted 51-50 to cancel a regulation issued by the Obama administration that would prohibit states from denying certain funds to health-care providers that perform abortions, freeing states to refuse to give the funds to Planned Parenthood Federation of America Inc. and similar organizations.