Washington (CNN) President Donald Trump, Vice President Mike Pence and other political leaders on Wednesday denounced the bombs sent to 2016 Democratic presidential nominee Hillary Clinton, President Barack Obama and CNN's New York bureau, among other locations.

"In these times we have to unify, we have to come together and send one very clear, strong, unmistakable message that acts or threats of political violence of any kind have no place in the United States of America," Trump said Wednesday at the White House.

The White House called the attempted attacks "despicable."

"The United States Secret Service and other law enforcement agencies are investigating and will take all appropriate actions to protect anyone threatened by these cowards," White House press secretary Sarah Sanders said in a statement.

Responding to a tweet from Pence, who said the administration condemned the "despicable" actions and that "those responsible will be brought to justice," Trump said on Twitter earlier, "I agree wholeheartedly!"

"President Trump's words ring hollow until he reverses his statements that condone acts of violence," the Democratic leadership said of Trump's remarks in a statement Wednesday. "Time and time again, the President has condoned physical violence and divided Americans with his words and his actions: expressing support for the Congressman who body-slammed a reporter, the neo-Nazis who killed a young woman in Charlottesville, his supporters at rallies who get violent with protestors, dictators around the world who murder their own citizens, and referring to the free press as the enemy of the people."

Former President Bill Clinton expressed gratitude to the Secret Service for responding to the suspicious packages.

"Thank you to the @SecretService and all law enforcement agencies who responded to this week's incidents," Clinton tweeted Wednesday afternoon. "They work tirelessly to keep our country and communities safe. I am forever grateful for their efforts."

Rep. Debbie Wasserman Schultz -- a Florida Democrat whose Sunrise, Florida, office was listed as the return address for the packages, including one that was addressed to former Attorney General Eric Holder and was returned to sender -- called for the attempted attacks to be "vigorously prosecuted."

"We will not be intimidated by this attempted act of violence," Wasserman Schultz said in a statement. "This appalling attack on our democracy must be vigorously prosecuted, and I am deeply disturbed by the way my name was used."

New York Democratic politicians condemned the attacks.

"This clearly is an act of terror attempting to undermine our free press and leaders of this country through acts of violence," New York Mayor Bill de Blasio said at an afternoon news conference about the package sent to CNN's office at the Time Warner Center in New York City.

New York Gov. Andrew Cuomo echoed the mayor, saying, "Terrorism only works if you let it work. We will not allow these terrorist thugs to change the way we live our lives."

National Counterterrorism Center spokesperson Maura Beard tells CNN that officials there have not yet concluded that there is a link to foreign terrorism with the suspicious packages.

The Secret Service said Wednesday it intercepted two "suspicious packages" addressed to Obama and Clinton it discovered during "routine mail screening procedures" earlier this week.

Bryan Paamann, an FBI special agent in charge of the counterterrorism division in New York, later said the devices inside appeared to be pipe bombs.

Pence said in his tweet he was "grateful for swift response" of the Secret Service, FBI and local law enforcement, who are investigating whether the packages intended for Obama and Clinton are connected to the package targeting major Democratic donor George Soros earlier this week.

"Let me be clear, we condemn these attempted acts of violence in the strongest possible terms," Pence said later, speaking at a campaign event in Pennsylvania.

The President's family -- first lady Melania Trump, the President's daughter and adviser Ivanka Trump and sons Donald Trump Jr. and Eric Trump -- condemned the threats.

"These terrorizing acts are despicable, and anyone responsible will be held accountable to the fullest extent of the law," Sanders said in a statement.

House Speaker Paul Ryan called Wednesday's attempted attack an "act of terrorism."

"Let me just say something that needs to be said on a day like today," Ryan told a crowd at a campaign rally in Mosinee, Wisconsin. He shushed the group as they began to chant "Build the wall."

"Did you see the news this morning about these devices?" he asked, as the crowd calmed down.

"That is an act of terrorism. There is no place for that in our democracy," Ryan said. "We reject that, and I just want to say thank God for our law enforcement who is doing this day in and day out to keep us safe."

House Majority Whip Steve Scalise, who was seriously wounded from a gunshot last summer, said the attempted attacks "are beyond criminal, they are acts of pure terror."

These attempted attacks that have been made are beyond criminal, they are acts of pure terror. Violence and terror have no place in our politics or anywhere else in our society. — Rep. Steve Scalise (@SteveScalise) October 24, 2018

"Violence and terror have no place in our politics or anywhere else in our society," the Louisiana Republican posted on Twitter. "I have experienced first-hand the effects of political violence, and am committed to using my voice to speak out against it wherever I can."

Scalise added that this "cannot become the new normal."

Republican Sen. Jeff Flake of Arizona, who was on the baseball field with Scalise during the 2017 shooting attack, warned that we are in "terrible times" and called for Americans to "tone down the rhetoric" on "both sides" of the aisle.

"We've got to tone it down. We've got to see people as opponents, but not enemies," Flake told CNN's Maria Santana outside the evacuated Time Warner Center on Wednesday morning.

Senate Majority Leader Mitch McConnell of Kentucky too condemned the incidents in a statement from his office saying, "As we continue to learn more, Americans are united in gratitude for the first responders — the Secret Service, the Postal Service, and other law enforcement — who protect our leaders and public figures from such unconscionable acts."

Asked whether discourse has contributed to increasing threats like the suspicious packages, Republican Sen. Orrin Hatch told CNN that there are "a lot of things" that have contributed to the rising political rhetoric, saying that "our society has become fairly complex."

The Utah Republican suggested that people "ought to moderate their positions, both sides."

Asked if that pertained to the President, who has labeled Democrats and media the enemy, Hatch said, "I don't see anything really wrong with the President. I think that he's in a tough position. He's getting attacked on all sides, so he ought to be able to express himself."

Republican Sen. Marco Rubio of Florida was forceful in his response, saying that an "attack on an American who happens to be a Democrat, Republican or independent is an attack on America."

"Some already giving in to temptation to react to this terror attack by either assigning blame for or rationalizing it," Rubio wrote on Twitter. "No sane or well intentioned person, no matter how partisan, would do this. It's either the work of a demented person or terror aimed at further dividing America."

Republican Utah US Senate candidate Mitt Romney urged Americans to rise above the political rancor he believes is behind the attempted attacks.

"Disgusting, vile threats and actions against fellow Americans and our institutions are sadly unsurprising: hate acts follow hate speech," the 2012 Republican presidential nominee tweeted . "It is past time for us to turn down and tune out the rabid rhetoric."

Democrats also called out the attempted violence.

Former Vice President Joe Biden called the country to come together.

"This division, this hatred, this ugliness has to end," he tweeted.

Democratic Sen. Chris Murphy of Connecticut blasted the attacks as a "coordinated assassination attempts against Democrats" and called for the perpetrator to be "prosecuted to the full extent of the law."

"Whoever is behind these attacks is trying to silence politicians and journalists from speaking truth," he said. "They won't succeed."

On Twitter, Democratic Sens. Tim Kaine of Virginia, Clinton's running mate in 2016, and Elizabeth Warren of Massachusetts said the threats have "no place in our free and lawful society" and "no place in our democracy."