( CNN ) -- Yemen 's embattled president , still recovering from a violent attack last month , met with a top U.S. counterterrorism official in Saudi Arabia Sunday . Yemeni state television broadcast footage of the president 's meeting with John Brennan , U.S. President Barack Obama 's top counterterrorism adviser . The two met at a military hospital in Riyadh , where Yemeni President Ali Abdullah Saleh has been recovering since he was wounded in the attack on his presidential compound more than a month ago . Video of the meeting shows Saleh wearing a suit jacket , his face still singed from the June 3 blast . Brennan wished Saleh `` a speedy recovery '' but also `` emphasized the importance of resolving the political crisis in Sanaa , '' the White House said in a statement on Sunday 's meeting . He urged Saleh to sign the Gulf Cooperation Council 's political transition plan for Yemen . `` The United States believes that a transition in Yemen should begin immediately so that the Yemeni people can realize their aspirations , '' the White House statement said . Saleh has voiced agreement with the plan by the GCC , which would ensure his gradual departure from office , but he has not signed it . Saleh told Brennan that the GCC initiative laid the groundwork for exiting the political crisis through national dialogue involving all political parties , Yemen 's state-run Saba news agency reported . As Brennan and Saleh met in Saudi Arabia , clashes erupted between government security forces and armed tribesmen in one of the epicenters of Yemen 's anti-government movement . Two people were killed and at least nine others were injured in the southwestern Yemeni city of Taiz Sunday , medical sources in the city said . Dozens of homes were also damaged in the fighting , which started early Sunday morning and stretched for more than eight hours , witnesses said . Saleh appeared on television in Yemen Thursday for the first time since the attack , telling viewers he was on the mend , open to talks with opposition forces and determined to strike back at his attackers . His speech from Saudia Arabia transfixed his home country , which has been enduring months of anti-government protests and al Qaeda in the Arabian Peninsula militant activity . Saleh said he had had eight successful surgeries in Saudi Arabia , but the president , whose badly burned face was dark and who sat stiffly upright in a buttoned-up robe , did n't specify when he would go back to Yemen -- a return his supporters anticipate but his opponents hope will never occur . The United States has been aiding Yemen 's military in its fight against Islamic militants amid fears that al Qaeda is exploiting the political chaos and leadership vacuum engulfing the unstable and impoverished Arabian Peninsula country . On Sunday , Saleh thanked Brennan for U.S. support of `` Yemen 's unity , security and stability , '' according to Saba . `` He confirmed that Yemen needs to be supported and assisted to promote economic and development fields so as to reduce poverty and unemployment , which represent a fertile environment of terrorism , '' Saba reported . CNN 's Yousuf Basil and journalist Hakim Almasmari contributed to this report .
NEW : Clashes erupt in the southwestern Yemeni city of Taiz . White House : `` A transition in Yemen should begin immediately '' Yemeni state television shows Saleh and Brennan meeting . Saleh has been recovering in Saudi Arabia since he was wounded in a June 3 attack .