"It just turned out that Pekka was the first one we were in position to negotiate with and bring to conclusion," team chairman Tom Ciggaran said Thursday in a conference call.
"We have every intent of signing both Shea and Ryan, and we're going to do everything we can to make that happen. These guys are sort of home-grown," Ciggaran said. "They're just people that we want to have around to be the core of a Stanley Cup-winning team for years to come."
Rinne had been set to become a restricted free agent July 1 along with Suter. Weber, also the team captain, will be a restricted free agent after being awarded $7.5 million through arbitration for this season.
Fans have criticized the Predators' ownership group for not spending big money on players, and this deal for Rinne easily is the biggest yet for a franchise that started as an expansion team for the 1998-99 season. Now the worry is whether the team has enough money left for Suter and Weber with an annual payroll usually closer to the NHL floor than the salary cap.
"The money is there to sign these guys, and we have every intent of doing it," Ciggaran said.
The Predators started with Rinne because general manager David Poile said he believes a team is built starting with great goaltending, just like baseball teams need good pitching.
"Pekka signing for this many years, I think it gives a terrific opportunity to be successful," Poile said.
Rinne, a native of Kempele, Finland, was second in voting for the Vezina Trophy and fourth in voting for the Hart Trophy earlier this year after helping the Predators win their first playoff series. He ranked second in the NHL with a .930 save percentage, third in goals-against average (2.12) and tied for sixth with six shutouts.
He leads the NHL with the most shutouts since 2008-09, and his 22nd last weekend against Anaheim also was his 100th career victory.
This season, Rinne became the first goalie in team history to start each of the first 11 games. He leads the NHL with 307 saves and is second in shots against (333) and third in minutes played (624:37). He said he wanted to stay in Nashville.
"You can only make choices on your own, and obviously I've had that luxury to play with those guys three years now," Rinne said during the call before the Predators play at Phoenix on Thursday night. "I want to keep elite players and I know we are doing our best to get them signed here. But this is my decision. I was the first one out of us three that signed, and hopefully those two guys are next."
Nashville drafted Rinne in the eighth round in 2004 with the 258th pick overall. Rinne also has played for Finland in the World Championships in 2009 and 2010.
Poile said he already has talked a couple times with Suter's agent, who will be coming to Nashville for more talks later in November. He also said he told both Suter and Weber of the deal Thursday morning. Both were happy for Rinne, and ideally the defensemen will be next.
"This is the first step in that process," Poile said.