Kevin Biggar and Jamie Fitzgerald were at 88 deg. 54 min. 02 sec. south and 85 deg. 20 min. 13 sec. west about to enter 89 deg. south, the pair reported on their web site.
"That is very exciting ... 1 degree to go!" Biggar, 37, wrote early Thursday local time.
"We expect it will take five more full days of towing and then we will arrive at the South Pole on the second of January, and we are pretty excited about that," he noted.
The pair, dragging sleds behind them over frequently rough terrain, are about to complete their trek to the world's most inhospitable southern point.
After a short celebration, they plan to turn around and head back to the Antarctic coast, to complete their journey of more than 2,400 kilometers (1,500 miles).
They are bidding to become the first team to walk to the South Pole and back unaided and without being resupplied.
The feat will mark the 50th anniversary of the founding of Scott Base, New Zealand's Antarctic research base on the southern continent.
Biggar, 37, noted in recent days they had been making progress at a slower 21.1 kilometers (13.2 miles) a day, "a bit of a shame because we were really hoping to keep up with our general 14 (nautical miles 24.6 kilometers/15.4 miles a day) all the way to the pole."
But thin air at 3,000 meter (9,850 feet) altitude on the Antarctic plateau and soft snow under foot had slowed their progress as soft snow conditions near the coast had done early in their journey.
Fitzgerald, 26, had also experienced some hamstring problems that had slowed the duo.
"In other regards it has been fantastic up here. The wind is very light, the sun is out and at last it is very flat with very little sastrugi (rough ice ridges)," Biggar wrote.
"It looks like it is going to be a long trudge one long flat trudge to the pole now," he added.
Their plan is to reach the Pole before Jan. 4 and then speed back to the coast, towed by kites, in time to catch the last plane departing Antarctica's Patriot Hills landing strip at the end of the month, reports AP.
"Our return journey will be faster as our loads will be lighter and we can use our powerful traction kites to take advantage of the prevailing wind," Biggar said.
They have three different sizes of kite to handle all wind conditions and hope to average 50 kilometers (31 miles) a day on the return journey.