"The results of these negotiations will be catastrophic for the interests and the security of Jordan and Egypt."
Mubarak and the Jordanian monarch have been invited to Washington to join a summit on September 2, during which Israel and the Palestinian Authority are due to resume direct talks for the first time in 20 months.
The Palestinian Authority broke off negotiations with Israel in December 2008, when Israel launched a three-week war in the Gaza Strip.
Palestinians 'not bound'
Meshaal said the Palestinian people "will not feel bound by the outcome of these negotiations, because the Palestinian negotiators renounced their demands".
Hillary Clinton, the US secretary of state, announced earlier that the talks will be held without preconditions, and will run for a year.
Meshaal asked Abbas and his Fatah faction to join Hamas in adopting a unified strategy, which he said would not drop diplomacy but would concentrate on the "option of resistance and holding on to inalienable Palestinian rights".
Abbas's negotiation strategy has long been condemned by Hamas, which seized control of the Gaza Strip from the Palestinian Authority in 2007.
Hamas and Fatah have been estranged for years, and Egyptian attempts at mediation over the last few months have produced little progress.