PARIS (Reuters) - Britain and the European Union should both show flexibility when London negotiates its future relationship with the bloc, U.S. Treasury Secretary Jack Lew said on Tuesday, warning Britain about a proposal to cut its tax rate.

Lew said after meeting French Finance Minister Michel Sapin in Paris that it was in the interests of all that talks between Britain and the EU produce a "highly integrated relationship".

"It is important that both sides demonstrate flexibility in order to produce an amicable and mutually-acceptable outcome," Lew told a news conference with Sapin.

"It is also critical that negotiations take place in a smooth, pragmatic and transparent manner," he said.

France is pressing for Britain to quickly seek formal negotiations with the EU about its departure in order to reduce the uncertainty its referendum has created.

French officials have also expressed concern that Britain has already raised the possibility of cutting its corporate tax rate further in order to remain competitive internationally after it leaves the EU, a concern Lew also appeared to share.

"We have to be very careful as we each make our own national policies not to take steps that create competitive pressures to drive down tax rates in a way that ends up becoming a magnate for the kind of activities that we are trying to curtail," Lew said.

Britain announced plans last week to cut corporate tax to less than 15 percent in an attempt to cushion the shock of the country's decision to leave the EU.

(Reporting by Leigh Thomas; Editing by John Irish)