MIAMI, Oct 18 (Reuters) - Hurricane Wilma triggered mudslides that killed up to 10 people in Haiti as the season's record-tying 21st storm strengthened rapidly on Tuesday and headed for the Gulf of Mexico on a path toward storm-weary Florida.

Wilma was expected to strengthen into a powerful Category 4 storm on the five-step scale of hurricane intensity, with winds over 130 mph (209 kph) by the time it crosses from the Caribbean Sea into the Gulf of Mexico on Friday.

The U.S. National Hurricane Center's long-range forecast track, which has a wide margin of error, had it crossing southern Florida on Saturday. The state was hit by four hurricanes last year and has been struck by Hurricanes Dennis, Katrina and Rita this year.

Wilma was the 21st tropical cyclone of the Atlantic hurricane season, tying the record for most storms set in 1933. It was also the 12th hurricane and tied the record for most hurricanes in a season, set in 1969. The season still has six weeks to run.

Days of steady rain from Wilma caused mudslides that killed at least seven people and as many as 10 in mountainous Haiti, government officials said.

Wilma threatened Honduras and Nicaragua with flooding rain, compounding the woes of Central America. More than 1,000 people in Guatemala and El Salvador were killed by landslides and floods triggered by Hurricane Stan this month.