(CNN) -- Washington -- one of the world's most secure cities -- is reacting cautiously following the attacks at Canada's Parliament Hill.
One soldier who was shot at Canada's National War memorial, located across from the Parliament building, has died. The gunman was shot and killed on the scene inside Parliament Hill's Center Block.
President Barack Obama spoke to Canada's Prime Minister Stephen Harper on the phone Tuesday afternoon.
"The President offered any assistance Canada needed in responding to these attacks. Prime Minister Harper thanked the President and the two leaders discussed the assault and agreed to continue coordination between our governments moving forward," the White House said in a statement.
Later this afternoon, the president told pool reporters that it is still unknown whether a "broader network or plan" was behind the shooting. He added that these attacks serve as a reminder to "remain vigilant" when dealing with unnecessary violence or terrorists.
"It's very important, I think, for us to recognize that when it comes to dealing with terrorist activity, Canada and the United States has to be entirely in sync. We have in the past and I am confident we will continue to do so in the future," the president said.
Secretary of State John Kerry was also briefed on the shootings, Mary Harf, the State Department's spokeswoman confirmed.
At the U.S. Capitol, which was the site of a deadly shooting in 1998, police are "monitoring and tracking" developments in Canada. But as of now, they haven't modified their regular "post 9-11 heightened state of alertness," according to U.S. Capitol Police spokeswoman Kim Schneider.
Congress is on recess until next month's elections, though the Capitol remains busy with tourists, staff and other workers.
Across the Potomac River, security near Arlington Cemetery has increased, specifically at the Tomb of the Unknown Soldier.
The U.S. Embassy in Ottawa, located near the Ottawa River next to Parliament Hill, is on lockdown, according to a message posted on Twitter. A spokesman at the Canadian embassy in Washington told CNN that they have locked the front door to non-embassy staff as a "precautionary measure."
In New York City, the NYPD added extra security to the Canadian consulate as a precaution.
NORAD, meanwhile, is increasing its alert posture and the number of planes ready to respond to a problem, according to CNN Pentagon Correspondent Barbara Starr. NORAD, which provides air defense over North America, is in continuous contact with Canadian law enforcement, CNN is told.
"We have taken appropriate measure to ensure that NORAD is postured to respond quickly if the ongoing situation in Ottawa should include any effect on aviation," NORAD spokesman Captain Jeff Davis said.
Washington was already reviewing its approach to security before the shooting in Ottawa. A man shocked the nation last month by allegedly jumping the fence outside the White House and making his way into the building before finally being stopped by security. Around the same time, reports emerged that a man with a gun rode the same elevator as Obama during a visit to the Centers for Disease Control and Prevention in Atlanta.
Those incidents prompted the resignation of Secret Service Director Julia Pierson.
In an interview with Roll Call published Wednesday morning before the Ottawa shootings, Terrance W. Gainer, the former Senate sergeant at arms, said the U.S. Capitol complex is too open.
"The only people that have left their campus open is the Capitol," Gainer said. "Now, I get people wanting to be open, but people have to somehow understand there are constant threats and if the only way to mitigate the threat is have an officer chase after the bad guy — you're going to end up having problems."
The Twitter account for the National Security Council also tweeted updates including that the president had spoken with Harper and condemned the attacks.
CNN's Barbara Starr, Jim Acosta, Kevin Liptak, Ted Barrett, Pam Brown, and Elise Labott contributed to this report.