"The Jewish Crusader coalition will not be safe anywhere from the fighters' attacks," said al-Qaeda's spokesman Sulaiman Abu Ghaith in an audio statement broadcast by the Qatari-based al-Jazeera television channel.
The statement, dated 6 December, was also posted on an Islamist web site - just days after al-Qaeda first claimed responsibility for the Mombasa attacks.
Kenyan officials say the country has been put on high alert following the statement and a new spate of terror threats.
On Monday, the British High Commission in Kenya reopened four days after what officials described as a specific terrorist threat to the building forced it to close.
Sixteen people, including three suicide bombers, were killed in the attack on the Israeli-owned Paradise Hotel, north of Mombasa. A missile attack on an Israeli passenger plane failed.
Kenyan police say they are planning to release pictures of the main suspects.
Change of tactics
Abu Ghaith - one the main suspects in the 11 September attacks on the US - warned of more and wider attacks on American and Israeli targets "on land, air and sea".
"We will hit the most vital centres and we will strike against its strategic operations with all possible means," the statement said.
Al-Qaeda does not usually claim direct responsibility for attacks, instead praising those who carry them out.
But Abu Ghaith said that members of the terror network "find ourselves today in better circumstances and a stronger position to do that".
Although the statement could not immediately be verified, US officials said they considered it to be credible.
Experts believe that al-Qaeda is increasingly relying on the use of the internet, which enables its members to communicate quickly and anonymously.
They say it is extremely difficult to trace and confirm postings attributed to al-Qaeda, as web sites themselves often disappear or change addresses.