* 21 American crew believed to be safe

* Attackers struck 400 miles (600 km) off Mogadishu

(Adds details, background)

NAIROBI, April 8 (Reuters) - Somali pirates seized a Danish-owned, U.S.-operated container ship on Wednesday with 21 American crew on board in the latest of a sharp rise in attacks off the Horn of Africa nation, a maritime group said.

Andrew Mwangura of the Kenya-based East African Seafarers' Assistance Programme said the 17,000 tonne vessel was hijacked in the Indian Ocean 400 miles off the Somali capital Mogadishu.

He said all the crew were believed to be safe, and that the vessel had been tentatively identified as the Maersk Alabama.

Gunmen from Somalia seized a British-owned ship on Monday after hijacking another three vessels over the weekend.

In the first three months of 2009 only eight ships had been hijacked in the busy Gulf of Aden, which links Europe to Asia and the eastern Indian Ocean through the Suez Canal.

Last year, heavily armed Somali pirates hijacked dozens of vessels, took hundreds of sailors hostage, often for weeks, and extracted millions of dollars in ransoms.

Foreign navies rushed warships to the area in response and have reduced the number of successful attacks in recent months. But there are still near-daily attempts and the pirates have started hunting further afield near the Seychelles.

On Monday, they hijacked a British-owned, Italian-operated ship with 16 Bulgarian crew members on board.

Over the weekend, they also seized a French yacht, a Yemeni tug and a 20,000-tonne German container vessel. Interfax news agancy said the Hansa Stavanger had a German captain, three Russians, two Ukrainians and 14 Filipinos on board.

The pirates typically use speed boats launched from "mother ships", which means they can sometimes evade foreign navies patrolling the busy shipping lanes and strike far out to sea.

They take captured vessels to remote coastal village bases in Somalia, where they have usually treated their hostages well in anticipation of a sizeable ransom payment.

Pirates stunned the shipping industry last year when they seized a Saudi supertanker loaded with $100 million worth of crude oil. The Sirius Star and its 25 crew were freed in January after $3 million was parachuted onto its deck.

Last September, they also grabbed world headlines seizing a Ukrainian cargo ship carrying 33 Soviet-era T-72 tanks. It was released in February, reportedly for a $3.2 million ransom. - For factbox on ships held, click on [ID:nL6183255]