The US space agency will try to launch Atlantis around September 7-8 if Tuesday's lift-off is cancelled at the Kennedy Space Center on Florida's eastern coast.
However launching next week could be problematic as it would conflict with a Russian Soyuz rocket mission to the ISS. NASA officials will talk with their Russian counterparts to find a solution.
But NASA officials remained hopeful they could launch the shuttle Tuesday at 3:42 pm (1942 GMT) on the first major ISS construction mission in nearly four years.
"We have really two competing objectives. One, we want to get the vehicle ready to go fly. The other objective is we want to get the vehicle ready to roll back to the VAB (vehicle assembly building)," said Bill Gerstenmaier, the associate administrator for space operations.
NASA made initial preparations to possibly move the shuttle back to the VAB as a hurricane that was later downgraded to a tropical storm barrelled across the Caribbean.
Storm threat
Forecasters said Tropical Storm Ernesto could regain hurricane strength before striking western Florida later this week.
"We would like to have the vehicle back in the vehicle assembly building before high winds hit the Cape, so that forces us to take some action fairly soon," Mr Gerstenmaier said.
Officials had already delayed earlier launch attempts to give engineers more time to determine whether a lightning strike on Friday had damaged ground and shuttle systems.
The orbiter and external fuel tank's hardware were cleared for launch, but engineers were given more time to check if the two solid rocket boosters were damaged.
Although lightning strikes are common on the launch pad, officials said Friday's was believed to be the strongest to hit the structure. The storm discharge struck a lightning protection rod atop the launch pad.
Once it launches, Atlantis will carry six astronauts and a new 16-tonne segment with two huge solar panels on the first of 16 flights planned to complete assembly of the half-finished space station by 2010, when the shuttle fleet is set to retire.
The 2003 Columbia shuttle explosion forced a halt in the orbiting laboratory's construction.
Third flight
The Atlantis mission will be the third shuttle flight since the Columbia disaster, which was caused by debris that struck its heat shield during lift-off, dooming its return home with seven astronauts aboard.
After two flights by the space shuttle Discovery in the past two years aimed at improving safety, NASA declared it was ready to resume construction of the station, which is key to US ambitions to send humans to Mars.
The Atlantis mission is a critical first step in the ISS's assembly. The installation of the solar panels, which will eventually provide a quarter of the station's power, is one of the most complex parts of the ISS assembly sequence.
Three spacewalks are planned during the 11-day mission, which will be followed by another shuttle flight planned for December for another assembly sequence that officials said would be even trickier.
The ISS currently weighs 197 tonnes and will be extended to a massive, 454-tonnes structure once it is completed.
The United States, Russia, Japan, Canada, Brazil and 11 countries of the European Space Agency are involved in the orbiting laboratory project, which was launched in November 1998.