US Secretary of State Rex Tillerson on Saturday urged Iranian President Hassan Rouhani to dismantle Tehran's "network of terrorism" and end ballistic missile testing, in Washington's first reaction to his re-election. 

"What I would hope, is that Rouhani ... use that (new) term to begin a process of dismantling Iran's network of terrorism, dismantling its financing of the terrorist network, dismantling the manning and the logistics and everything that they provide to these destabilising forces that exist in this region," Tillerson said in Riyadh.

"We also hope that he puts an end to their ballistic missile testing," Tillerson said at a joint press conference with his Saudi counterpart, on the first day of a visit by President Donald Trump to Saudi Arabia.