Sea survivor too frail to go home
Mr Alvarenga, 37, washed ashore late last month. He was taken last week to the Marshall Islands' capital, Majuro, where he has been resting at a hotel.
Mr Dalton arrived in Majuro late on Friday and met Mr Alvarenga and local officials.
"At this moment, there are no travel plans or definite itinerary," he said. "His return will depend of when his health allows the long journey back."
Mr Alvarenga's spritely appearance on Monday while greeting hundreds of well-wishers in Majuro had many questioning his story.
He earlier told officials he left Mexico in late 2012 with another fisherman, who later died, for a day of shark fishing when a storm threw them off course and they began drifting.
But Mr Alvarenga looked much weaker on Thursday during a brief public appearance at the hotel, and had to be assisted into the room by two people while others stood by ready to help.
Officials said then that Mr Alvarenga needed to be taken back to hospital for more medical checks and that it would probably be three or four days before he was fit enough to travel back to El Salvador.