ISLAMABAD, Pakistan — Afghanistan's Taliban insurgents rejected an offer of talks from Kabul on Monday and threatened for the first time to strike a target in the West, suggesting many years of violent conflict to come.

The United States also shot down the Afghan government proposal and said it wouldn't support such an initiative — worsening the strain in U.S.-Afghan relations. The major beneficiary of the dispute appears to be the Taliban, which said it wouldn't come to the negotiating table until all foreign troops left Afghanistan