* Delegates at Ethiopia talks meet mediators, but not each other
* Fighting reported outside Jonglei state capital
* More than 1,000 people killed since start of violence (Updates with U.S. evacuations in paragraphs 14-15)
By Carl Odera and Aaron Maasho
JUBA/ADDIS ABABA, Jan 3 (Reuters) - South Sudan's government and rebels finally began talks to end weeks of bloodletting on Friday after days of delay as the United States ordered out more of its embassy staff.
However, there was no face-to-face meeting, and fighting was reported near the key town of Bor, suggesting that a halt to clashes between President Salva Kiir's SPLA government forces and rebels loyal to former vice president Riek Machar is still a long way off.
Neighbouring countries fear that the fighting, which quickly spread out from the capital Juba last month along ethnic faultlines, could destabilise East Africa, and the regional IGAD grouping is mediating the peace talks in Ethiopia.
The talks had been scheduled to begin in Addis Ababa on Jan. 1, and made a slow start on Friday.
"Both delegations are meeting the mediators separately," said Dina Mufti, a spokesman for Ethiopia's Foreign Ministry. "We hope to bring both sides into face-to-face talks soon."
Meanwhile the SPLA said its troops were fighting rebels 24 km (14 miles) south of rebel-controlled Bor, the capital of the vast Jonglei state and site of an ethnic massacre in 1991.
Bor lies 190 km (118 miles) to the north of Juba and has changed hands three times since the unrest began.
"The rebels will be flushed out of Bor any time," SPLA spokesman Philip Aguer said.
Rebel spokesman Moses Ruai Lat, based in the northern state of Unity, said it was the government forces who were on the back foot and his advancing comrades were already "close" to Juba.
More than a thousand people have been killed and 200,000 driven from their homes in three weeks of fighting that has raised the spectre of a civil war pitting Kiir's ethnic Dinkas against Machar's Nuer.
The United States has been withdrawing non-essential embassy staff since mid-December and said Friday it was evacuating more.
It also urged all American citizens to leave South Sudan - a country the size of France estimated to hold the third largest oil reserves in sub-Saharan Africa, but desperately poor and short of infrastructure.
"We are not suspending our operations. We are just minimising our presence," said Susan Page, the U.S. ambassador.
More than 440 U.S. officials and private citizens have been evacuated on charter flights and military aircraft, State Department spokeswoman Marie Harf said in Washinton. The United States has also flown out 750 citizens of 27 other countries.
The Pentagon sent two KC-130 aircraft to pick up approximately 20 U.S. diplomatic personnel from the embassy in Juba, said Army Colonel Steve Warren, a spokesman. One landed and the other one circled nearby in case it was needed.
An emergency message to U.S. citizens on the embassy's website said the move was due to a "deteriorating security situation". It said there would be an evacuation flight on Friday arranged by the U.S. State Department.
Kiir has accused his long-term political rival Machar, whom he sacked in July, of starting the fighting in a bid to seize power. Machar denies the claim.
Mediators say Kiir's government and the rebels loyal to Machar have agreed in principle to a ceasefire, but there is no agreement on a starting date and some diplomats say both sides still seem more intent on manoeuvring for military advantage.
The United Nations said it was planning for the number of displaced people to double in the next three months. (Additional reporting by Richard Lough in Nairobi and Tom Miles in Geneva, Doina Chiacu and David Alexander in Washington; Writing by Richard Lough; Editing by Kevin Liffey and Andrew Hay)