Meshaal, saying he expected an Israeli attack to be launched soon, said: "We in Hamas are also preparing ourselves for battle, and we expect hot months."
He urged all other Palestinian groups to also "seriously prepare themselves for battle".
The US document, recently given to Israel and the Palestinians, calls on Israel to remove many West Bank roadblocks, improve operations at Gaza's crossings and arrange for a truck convoy between the West Bank and Gaza, two areas separated by Israel.
The Palestinians are asked to stop firing rockets from Gaza at Israel and prevent weapons smuggling into the coastal strip.
Israel is urged to allow weapons and equipment to reach security forces loyal to Mahmoud Abbas, Hamas' Palestinian president.
Most of the points were already contained in a November 2005 agreement, brokered by Condoleezza Rice, the US secretary of state, following Israel's pullout from Gaza.
Setting a timeline, albeit non-binding unless both sides accept it, is the main new element of the document.
Erekat said the Palestinians welcomed the timeline as the only way to translate words into action.
The document has already drawn the ire of Palestinian fighter groups involved in rocket attacks against Israel.
Abu Abeer, spokesman for the Popular Resistance Committees, said on Saturday: "The US plan does not serve our people's interests. The Committees will work to make it fail."
On Friday, Meshaal, told a rally in Syria that the Palestinians should not agree to halt rocket fire in exchange for an easing of travel restrictions.
Meshaal said: "I swear it's a farce ... the equation has now become: dismantling the checkpoints, in exchange for [giving up] resistance.
"This has become the Palestinian cause."
Erekat said Meshaal's comments were premature.
Abbas was due to head to Gaza on Sunday to brief Ismail Haniya, the Hamas prime minister, on the document.
Meshaal and other Hamas leaders have threatened a third Palestinian uprising if the international community does not lift its sanctions on the Palestinian government, imposed after Hamas came to power last year.
Meanwhile, fighters in the Gaza Strip fired three rockets towards Israel on Saturday, damaging a house in the town of Sderot.
The attack was said to have been made to avenge the killing of three members of the group by Israeli undercover troops in the West Bank a day earlier.