A dispute over plans for the bridge has re-introduced a sour note into a relationship that has improved markedly in the past two years since the retirement of Malaysia's former prime minister Mahathir Mohamad.
Mahathir's successor Abdullah Ahmad Badawi was reported over the weekend to have given his approval to the new bridge, but Singapore quickly responded by saying talks were still going on and "we should not prejudge the outcome".
Singapore's Foreign Ministry also stressed that the two countries had already agreed "it would not be helpful to publicise the details of these discussions".
A ministry spokesman said senior officials from the two sides were to meet for two days starting on Wednesday in Malaysia's administrative capital Putrajaya, near Kuala Lumpur.
Malaysia's New Straits Times newspaper reported on Sunday that Abdullah had given approval for the new bridge to replace the causeway, which is more than 80-years-old and often choked with traffic.
In 2000, the cost of a new bridge was estimated at about $170 million with the two countries splitting the bill evenly, it said.
"Although the new bridge issue has not been resolved, we believe it can be done through consultation"
Syed Hamid Albar,
Malaysian foreign minister
A modern bridge bypassing urban centres - known as the Second Link - already operates between Malaysia and Singapore in the west, but the historic causeway, which goes directly into southern Malaysia's Johor Bahru city, is still favoured by many motorists.
The report said Malaysia wants to start work on its half of the new bridge even though Singapore has yet to announce plans to build the other half over the narrow Johor Strait that separates them.
Last year, the two neighbours signed an agreement to settle a long-running dispute over Singapore's land reclamation works, seen as a landmark decision marking a new thaw in relations.
"The government wants the formula and spirit of cooperation shown in settling the land reclamation issue to be used again by Singapore to settle the new bridge issue," Malaysian Foreign Minister Syed Hamid Albar was quoted as saying by the official Bernama news agency on Monday.
Abdullah has given his approval
for construction of the bridge
"Although the new bridge issue has not been resolved, we committed to building a new $540 million customs, immigration and quarantine complex that would serve traffic from the new bridge," he said.
Other issues between the neighbours include long-term water supply to Singapore, Singapore's military access to Malaysian airspace, the future of Malaysian-owned railway land inside Singapore and rival claims to a rocky islet.
Relations have periodically been rocked by disputes since Singapore was ejected from the Malaysian federation in August 1965 but Mahathir's retirement in October 2003 was seen as an opportunity to get rid of old animosities.