An air carrier Captain reported that after his aircraft was pushed back in FLL a foreign carrier crew taxied a B737 between his aircraft and another aircraft parked in the next gate. The wing tips were very close.

Narrative

We pushed back from our gate in FLL. The ground crew positioned the aircraft just right of the taxi line with the right wing just abeam the next gate. We started the #1 engine [to] set up for a single engine taxi. The ground crew disconnected and gave the all clear sign. We called for taxi and were cleared to taxi. We cleared left and right; but the First Officer noted that our two wing walkers had stopped just forward of the right wing and were looking aft. The First Officer said there was a B-737 trying to taxi between our aircraft and the aircraft parked on the next gate. We held position and waited for the B-737 to pass. We estimate the wing tips were within 5 FT of each other and no wing walkers. The ground crew should be able to tell you how close the wing tip was to the tail of the aircraft parked at the next gate. This was clearly a careless and reckless action on the part of the foreign air carrier's flight crew. FLL Ground must have cleared the flight to taxi but did not tell him the follow our flight.