Singapore's founding father Lee Kuan Yew (
Malaysia has demanded an apology over the claims -- made earlier this month -- which Abdullah said could inflame racial tensions in the multicultural country.
"I am sorry that what I said has caused you a great deal of discomfort," Lee said in a letter published by the New Straits Times.
"After a decade of troubled relations with your predecessor, it is the last thing I wanted," Lee continued.
"I had no intention to meddle in your politics. Indeed I do not have the power to influence Malaysia's politics or to incite the feelings of the Chinese in Malaysia," he said in the letter dated Sept. 29.
"Since you took over as prime minister in November 2003, relations between our two countries have much improved. Singaporeans and, I believe, Malaysians too, appreciate this," he added.
Lee, Singapore's former prime minister, who now serves in the cabinet of his son, Prime Minister Lee Hsien Loong (
He also said it was vital that Singapore, which is predominantly ethnic Chinese, stand up to its majority Muslim neighbors Malaysia and Indonesia.
Issues related to race, religion and education are extremely sensitive in Malaysia even after almost half a century of independence from British rule.
Malaysian Foreign Minister Syed Hamid Albar had called for an apology from Singapore, saying that Lee had overstepped the boundaries.
Malaysia and Singapore have strong economic ties but the two nations have squabbled periodically since Singapore was ejected from the new Malaysian federation in 1965 due to race politics.
Malaysia's 26.6-million-strong population consists of approximately 60 percent Malay Muslims, but the economy is largely controlled by ethnic Chinese, who make up some 26 percent of the population.