A federal court has allowed Tennessee to ban abortions as early as six weeks into pregnancy, while a Texas judge temporarily blocked enforcement of that state's decades-old ban on virtually all abortions, in a flurry of activity set off at courthouses across the US by the overturning of Roe v. Wade.

Statewide bans or other restrictions that were either left on the books for generations, tied up by legal challenges or specifically designed to take effect if Roe were to fall are now in play as a result of last week's Supreme Court ruling eliminating the constitutional right to terminate a pregnancy.

Roughly half the states are expected to prohibit or severely limit the procedure now that the high court has left it up to them.

Since Friday, judges have agreed to allow bans or other restrictions to take effect in Alabama, Ohio, South Carolina and Tennessee.

But abortion bans remained temporarily blocked in some states, including Louisiana, Texas and Utah.

Decisions are pending in other places, including Florida and Indiana. Abortion rights advocates also dropped some of their legal efforts in Indiana, Minnesota and Missouri.

Some clinics initially turned patients away soon after the high court ruling came down, but then reopened as judges ruled in their favour. That happened in Louisiana on Tuesday.

In Houston, a Democratic city in a conservative State, a judge blocked enforcement for now of a statewide ban on virtually all abortions.

Abortions in Texas are still prohibited at about six weeks because of a law that took effect last year.