Hoteliers also said that at least 400 tourists had checked out of hotels along the Indian Ocean coast.
Kenya called the alerts "unfriendly", saying they would increase panic and play into the hands of those behind the gun and grenade assaults that have hit the capital Nairobi and the Indian Ocean city of Mombasa, a tourist magnet.
Explosions in Nairobi and Mombasa on the weekend of May 3-4, one of them at a luxury seaside resort, killed seven people and Kenya has blamed this as well as other attacks on the al Qaeda-linked Somali group al Shabaab.
The Islamist movement killed at least 67 people including foreigners in a raid on a Nairobi shopping mall in September, saying it was in revenge for attacks on its fighters by Kenyan troops in Somalia.
The warnings and departures by tourists from hotels along the popular coast may further damage Kenya's tourism sector, one that President Uhuru Kenyatta said is "on its knees" following the series of deadly attacks.
Karanja Kibicho, the principal secretary at the foreign affairs department, said Kenya was assuring its visitors of "utmost security and safety", and lamented the advisories by countries also involved in its fight against the militants.
"The advisories therefore are obviously unfriendly acts coming from our partners who have equally borne the brunt of global terrorism and no doubt understand the repercussions of terror menace," Kibicho said.
Kenyan authorities say they do not know of any imminent threats at the coast. "The threats are perpetual, we are at war. But we have not received any specific threat on the hotels or other key site at the coast," said Interior Ministry spokesman Mwenda Njoka.
Njoka said police presence had been increased at the coast. However, this has not prevented tourists from leaving. At least 400 tourists checked out from their hotels heeding the travel advisories, according to Sam Ikwaye of the Kenya Association of Hotel Keepers Caterers. "They have cut short their stay and are leaving the country today (Thursday) and tomorrow. We fear many more will leave," Ikwaye told Reuters.
Adam Sheikh, a senior tourist official in Kenya's South Coast, said in Mombasa that planes had been chartered to fly the departing tourists from the coast.
"A plane was sent from London yesterday to pick the British nationals (up) from Mombasa. It will leave today at 6 p.m. (1500 GMT). Another plane will fly out the remaining tourists tomorrow at 11 a.m.," Sheikh said at a press conference attended by tourism officials drawn from various parts of the Coast region.
Tourist arrivals in Kenya have fallen as visitors stayed away, worried about the possibility of trouble around elections in March, which in the event passed off peacefully. Britain is Kenya's largest source market for the visitors.
The tourism sector employs 150,000 people in a country hard up for jobs. Travel agents said they hoped other tourist destinations in the Maasai Mara National Reserve in the great Rift Valley and around Mount Kenya could see more visitors.
Western diplomats have privately said Kenyan security forces - which receive aid and training from the United States, Britain and Israel among others - are weakened by inter-agency rivalries that hamper intelligence work.
Britain's Foreign Office told its citizens they should avoid travel to Mombasa and the surrounding area because of "recent terrorist attacks and the continuing terrorist threat in the area", unless travel was essential.
The U.S. Embassy warned its citizens of the continued threat of "potential terrorist attacks in the country," citing targets include hotels, nightclubs and malls. Kenya said Australia and France had issued similar warnings.