Con Ed and Utility Workers Local 1-2 spokesman John Melia say the parties are meeting.
Melia said Monday the meeting is to see if negotiations can resume.
Talks broke down Sunday after the workers' contract expired at midnight.
Both sides say there are many issues on which they have not reached agreement, including changing pension terms.
"Con Ed must end its lockout and allow the workers to return to their jobs while the new contract is negotiated," City Council Speaker Christine Quinn said in a statement Monday.
"When the power goes out and air conditioning and lights go off, it is often the most vulnerable such as the elderly and chronically ill that suffer with often serious consequences," the speaker said.
On Monday, union workers' tempers rose along with the heat on city streets.
"Kevin Burke, come out with your hands up, we want our pensions!" mechanic John Lucchini yelled into a bullhorn, naming Con Ed's CEO amid a protest in front of company headquarters.
Elsewhere in New York City, union leaders planned their next move following the breakdown of contract talks Sunday after a midnight deadline.
Both sides said there are many issues on which they have not reached agreement, including changing pension terms.
Con Ed offered workers a two-week extension, on condition they promise not to suddenly strike during that time. The union refused, and the utility declared a lockout, saying 8,500 workers would be replaced by 5,000 managers to keep services running.
The unionized workers told the company they'd be willing to work without a contract to keep the power company running, said union spokesman John Melia, who disputed the company's claim that its managers could do the job of the union workers.
A manager doing routine Con Ed work suffered minor burns, Con Ed confirmed.
Manhattan Borough President Scott Stringer issued a statement, saying Con Ed employees "deserve respect and a fair contract, and residents of the New York City region deserve assurances their power will continue without interruption as the heat wave continues."
He said both goals can be achieved "if we work together and settle this dispute amicably."
Another mechanic, Rick Brown, said there's nothing workers would like to do more than "than be on the clock."
But "the people who are doing the public an injustice are management," he said.
Brown was part of the noisy scene outside Con Ed headquarters near Union Square that included a chorus of honking, cheers and whistling heard a couple of blocks away. The honking was a show of support by drivers passing about 200 union demonstrators.
Many union workers wore T-shirts that said, "If we go out, the lights go out." They also featured a cracked, yellow light bulb with a red circle and slash.
Boos, catcalls and foul language erupted as management workers left the building.
Gregory Stephenson, a government relations employee at Con Ed who exited the company's corporate office to a loud chorus of boos, said he was disappointed by demonstrators' behavior.
"I understand the union's sentiment, but once you start to hurl abusive language - I just think there needs to be a level of decorum and respect," he said.
Con Ed closed walk-in centers, suspended meter readings and limited work on major construction projects in New York after the talks broke down around 2 a.m. Sunday, a couple of hours after the existing contract expired. The impasse came as New York endured more high temperatures that increased demand for air conditioning among the utility's 3.2 million customers.
There were about 200 outages overnight, nearly all of which were resolved by morning, Con Ed spokesman Chris Olert said Monday. He said management personnel were standing by, ready to address any problems.
Temperatures are expected to be in the high 80s and low 90s throughout the week.
The extreme weather included vicious storms from Indiana to New Jersey and south to Virginia that left 17 people dead and 2.7 million without power. Most of the damage came in the mid-Atlantic region, and only scattered outages across Con Ed's service area in New York were reported as of Sunday. Con Ed said it is keeping a close watch on its system and has trained managers working on essential operations.
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Associated Press Writer Alex Katz contributed to this report.
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