Protesters from Cross Lake First Nation want a revenue-sharing agreement with Manitoba Hydro, as well as a public apology, a shoreline cleanup and help with residential hydro bills which hover around $600 a month in the winter.
The First Nation has some long-standing concerns that need to be addressed, Selinger said.
"Some of these concerns are long-standing issues that go back several decades," he said in an interview with The Canadian Press on Thursday. "They're asking for that to be paid attention to.
"We all believe in a spirit of reconciliation around these long-term flooding issues that happened decades ago, and we need to continue working on them."
While Selinger was enthusiastic about energy efficiency programs to lower the cost of hydro bills in the community, he said bringing in a revenue-sharing agreement is more complex.
"It's not easily done but we think there's (a) possibility of doing that and we're open to that discussion as we go forward."
Cross Lake Chief Catherine Merrick said Manitoba Hydro has violated her people's treaty rights and must make amends. The band signed an agreement in 1977 after the Jenpeg dam was built, but Merrick said the Crown corporation and the provincial government haven't fulfilled their obligations.
Traditional lands are regularly flooded and the fragile shoreline is eroding, Merrick said. A handful of Cross Lake residents are employed by the dam, but there are none of the promised programs to "eradicate mass poverty and mass employment."
"If you're not going to be kind to my people, then we'll take back our land," she said Thursday before a rally at Manitoba Hydro's headquarters in Winnipeg. "That's exactly what we did."
Hundreds of protesters from the First Nation north of Lake Winnipeg marched to the hydro dam a week ago. While they have allowed employees to leave, Manitoba Hydro personnel have not been allowed to enter.
The dam is a stone's throw from the community, Merrick said, but many people get disconnected because they can't pay their bills. The dam employs about 10 people from the Cross Lake community.
"If my people were able to work, they would be able to pay their hydro bills," she said. "Our elders, their average income on their pension is $1,200 a month. They pay between $600 to $700 on their hydro bill."
The occupation at Jenpeg is peaceful but will continue until there's some real progress, Merrick said.
Hydro President Scott Thomson and Stan Struthers, cabinet minister responsible for the corporation, met with protesters at the site. But Merrick said they want a visit from Selinger, who bowed out of a planned trade mission to China because of the occupation.
But he hasn't directly contacted the protesters, she said.
Selinger wouldn't say whether he plans to go to the site for a meeting.
"I'm certainly keeping an open mind on that as we work our way through the process."
Manitoba Hydro spokesman Scott Powell said employees are still working at the dam and it continues to operate. The utility is continuing to work with the First Nation, as well as with the federal and provincial governments, to resolve the situation, he said.
"Things are moving forward," Powell said. "The factors underlying the whole situation are pretty complex and they've got a long history. When they involve so many different parties, it's a complex situation."
Jenpeg, which cost $310 million to build, is about 525 kilometres north of Winnipeg and is key in Manitoba Hydro's northern electricity generation. The dam helps regulate the level of Lake Winnipeg, which has become swollen in recent years due to flooding. It also acts as a reservoir for other northern generating stations.