The launch from Cape Canaveral in Florida had been scheduled for 1851 local time (2251 GMT).
If the shuttle is unable to launch by Wednesday it will have to wait until the end of the month to make way for a Russian cargo ship.
Earlier launches were called off because of lightning and fuel leaks.
Meteorologists have been predicting further heavy showers and lighting near the launch site on Monday and over the next couple of days.
"The weather has just bitten us again," launch director Pete Nickolenko told the crew, who had gathered in the shuttle for the lift-off.
New experiments
The Endeavour crew is set to install an external platform on Japan's space station lab, Kibo.
The orbiter is taking a seven-strong crew into space, made up of six Americans and one Canadian - Julie Payette - who will operate the shuttle's robotic arm during the mission.
Their arrival will bring the total crew on the outpost to 13 - a record for the International Space Station (ISS).
During five spacewalks, a platform will be added to the Japanese lab complex, which can be used for experiments that require materials to be exposed to the harsh environment of space.
In addition, Endeavour will deliver a new long-stay US crew member, Tim Kopra, to the ISS and bring back Japan's Koichi Wakata, who has lived aboard the platform for more than three months.
The space station, now about the size of a four-bedroom house, has been under construction for more than a decade.
When it launches, Endeavour will make the 127th space shuttle flight, the 29th to the station, the 23rd for Endeavour and the third in 2009.
Seven further flights to the platform remain before the shuttles retire in 2010.
