Two boats carrying heavily armed pirates opened fire on the 10,000-tonne Seabourn Spirit on Saturday morning about 160km off the Somali coast, in an apparent effort to seize control of the ship.
The ship managed to repell the attack with just one crew member sustaining minor injuries.
Andrew Linnington, of the National Union of Marine Aviation and Shipping Transport (Numast), which represents merchant navy officers, said the incident illustrated how the security situation in the area was close to being out of control.
He said the union would be holding urgent talks with ship owners this week to discuss the problem of piracy.
Linnington said there had been 23 reported attacks off the Somali coast since March, including attacks on two UN ships carrying relief supplies.
"We believe there should be a naval task force, particularly off Somalia, to try and stop the attacks. In the last 10 years hundreds of seamen have been killed and thousands injured in pirate attacks across the world," Linnington said.
There have been attacks on UN
ships carrying aid
"It's got to the stage where it's anarchy on the sea waves and this latest incident shows it's time governments got their acts together."
The call came as passengers from the Seabourn Spirit gave their accounts of the attack.
Woken by machinegun fire and a rocket-propelled grenade crashing into ship, several passengers reported how they looked on in disbelief as the pirates tried, but eventually failed, to seize their vessel.
"I was awake doing some work when I heard what sounded like a crack from outside at 5.50am," Norman Fisher, from London, told Britain's Press Association news agency.
The pirate attack took place 160
kilometres off Somalia's coast
"I looked out of the window and saw a small boat with about five people in it about 20 yards away.
"One of them clearly had a rifle. Later I realised that two of them had rifles and one had some kind of rocket launcher," he added.
The Bahamas-registered Seabourn Spirit was sailing towards the Indian Ocean port of Mombasa, Kenya, on a 16-day cruise out of Alexandria, Egypt.
Fisher said the captain, Sven Erik Pedersen, tried to ram one of the pirates' speedboats in an attempt to capsize it and stop them from getting aboard.
"The captain didn't sound the usual alarm because he was worried that people would run up on the deck thinking it was a fire, and that would be the worst place to be," Fisher explained.
"It's got to the stage where it's anarchy on the sea waves and this latest incident shows it's time governments got their acts together"
National Union of Marine Aviation and Shipping Transport
"Instead he made an announcement at five past six, saying: 'Stay inside, stay inside, we are under attack'."
After repelling the pirates, Pedersen explained the situation to passengers and was greeted with a round of applause, he added.
"It was all a very surreal experience - not the kind of thing you expect on a cruise," Fisher recalled.
Tourism chiefs scrambled to avert a public-relations disaster amid fears turmoil in Somalia could blight the region.
"This was well away from our waters. There is no threat," said Jake Grieves-Cook, chairman of Kenya's Tourist Board.
The cruise ship cancelled its planned stop in Mombasa and instead headed for the upmarket tourist islands of the Seychelles instead.
The attack was a dramatic introduction to Africa's most chaotic state.
Peace prospects are clouded by splits in the international community on how to reconcile Somalis.
"This ship incident shows the high importance of stabilising Somalia. We can ill afford to quibble while Somalia burns," said African Union envoy Mohammed Ali Faum.
Last month, UN monitors said a new government and its enemies were gearing up for a military showdown after buying up a vast array of weaponry this year.
Experts say it is hard to gauge how much piracy actually goes on. Many shipping firms do not report incidents, or ransoms paid, for fear of raising their insurance premiums.