* U.S. wants peacekeepers on the ground to stop killings
* The fighting has exacerbated ethnic tensions
* Many thousands killed, more than 1 million fled their homes (Inserts letter from senators in paragraph 17)
By Phil Stewart and Aaron Maasho
ADDIS ABABA, May 1 (Reuters) - U.S. Secretary of State John Kerry warned on Thursday that South Sudan's conflict could descend into genocide, as he renewed threats of sanctions and raised hope that more peacekeeping forces could be deployed swiftly to halt the bloodshed.
Kerry, emerging from talks about the increasingly ethnic slaughter in South Sudan with foreign ministers from neighbouring Ethiopia, Uganda and Kenya, said all sides agreed the "killing must stop."
"A legitimate force that has an ability to help make peace needs to get on the ground as rapidly as possible," Kerry said in Addis Ababa at the start of an African trip.
Addressing reporters later, Kerry said the goal was "in these next days, literally, we can move more rapidly to put people on the ground who could begin to make a difference."
His Ethiopian counterpart, Foreign Minister Tedros Adhanom, said all sides stressed the need for deployment of a force "as soon as possible."
A spokeswoman said Kerry was referring to regional forces under the authority of the United Nations, which already has a mission in South Sudan. Kerry said he and his African counterparts agreed on "the terms and timing and manner and size" of such a force but declined to offer details.
"The greatest single difference will be moving rapidly with U.N. Security Council imprimatur of support to get forces on the ground who could begin to separate people and provide safety and security. That's imperative," Kerry told reporters.
More than 1 million people have fled their homes and thousands of people have been killed since fighting erupted in December between troops backing President Salva Kiir and soldiers loyal to his sacked deputy, Riek Machar.
The fighting has exacerbated ethnic tensions between Kiir's Dinka people and Machar's Nuer.
Negotiations between the Kiir government and rebels loyal to Machar have failed to advance since the Jan. 23 signing of a ceasefire that never took hold.
Asked about the risk of genocide, Kerry said "very disturbing, leading indicators of the kind of ethnic, tribal, targeted nationalistic killings" raised troubling questions.
"Were they to continue in the way that they have been going (they) could really present a very serious challenge to the international community with respect to the question of genocide," he told reporters.
Delegations from both sides in South Sudan resumed face-to-face discussions in Addis Ababa on Thursday after several delays, officials said.
A senior State Department official, speaking to reporters traveling with Kerry ahead of the trip, said regional powers were losing patience with the inability of both sides in South Sudan to move forward with peace efforts.
"I think both sides think that they can win this militarily, and they have certainly not participated in any committed way to finding a negotiated settlement for the conflict," the official said, speaking on condition of anonymity.
Kerry also renewed U.S. threats of sanctions and said regional partners Uganda, Kenya and Ethiopia also "accepted the responsibility for also doing sanctions."
U.S. lawmakers are also pushing the Obama administration to do more. A group of nine Democratic and Republican senators wrote to President Barack Obama on Thursday, urging him to impose sanctions on those responsible for human rights abuses, work to strengthen the mandate of the U.N. South Sudan mission and hold Kiir and Machar accountable for progress in peace negotiations.
Many South Sudanese own property in the three neighbouring countries and regularly travel there, the State Department official said.
Obama earlier this month authorized possible targeted sanctions against those committing human rights abuses in South Sudan or undermining democracy and obstructing the peace process.
Still, Kerry held out hope that talks might sway the course of events in South Sudan and pointed to Kiir's decision last week to release four political prisoners.
"We are hoping that now opens up the possibility of a mediation and dialogue that could take place anywhere in the next few days," he said. (Reporting by Phil Stewart, additional reporting by Patricia Zengerle in Washington; Editing by James Macharia, Andrew Heavens and Ken Wills)