There has been a "rapid deterioration" in the Venezuelan situation, the centre founded by former US President Jimmy Carter has warned.
The authorities have vowed to find those responsible
The Carter Center says it "deplores the escalation of violence" in the capital Caracas over the last week, which culminated in bomb attacks on Spanish and Colombian embassy buildings early on Tuesday.
Security has been tightened around foreign buildings in Caracas since the bombings, which injured three people and caused some damage.
Responsibility for the bombings is unclear, with government officials suggesting they were intended to destabilise the Hugo Chavez administration and US officials highlighting that they followed "verbal attacks on the international community" by Mr Chavez.
The statement from the Carter Center called for the international community to "redouble support for all the initiatives designed to produce a peaceful, democratic... solution to the present crisis".
"We believe that verbal violence and threatening tone of political leaders, amplified by the media, encourage violent behaviour," said the statement.
It urged "President Hugo Chavez and the leaders of the opposition Coordinadora Democratica, as well as the chiefs of the media" to sign up to a declaration committing all parties to peaceful means of resolving the crisis.
However, efforts to mediate such a peaceful solution to the power struggle between elected President Chavez and his opponents - largely from business and middle-class backgrounds - by the Organization of American States, have faltered.
Carter's proposals failed to resolve the impasse
Mr Carter visited Venezuela in January in an attempt to suggest ways to resolve the impasse, which saw leaders of a nine-week strike demanding that Mr Chavez call fresh elections less than half way into his six-year mandate.
But constitutional restrictions and a reluctance on Mr Chavez's part to hold an immediate referendum on his presidency have hampered negotiations.
Mr Chavez has also been buoyed by the disintegration of the opposition strike and barricade on the country's crucial oil exports.
Last week, he sanctioned the arrest of one of the protest leaders, Carlos Fernandez, who is now under house arrest accused of treason and civil rebellion.
Then in his weekly broadcast on Sunday, Hello President, Mr Chavez told the world community to stop interfering in Venezuelan affairs.
Speaking to the governments of Colombia and Spain - whose embassies were targets in this week's bomb attacks - and the United States, among others, Mr Chavez said: "We don't meddle in your affairs; please don't meddle in ours."
Official US response to the bombs, by State Department spokesman Philip Reeker, simply "noted [they] follow sharp verbal attacks by President Chavez on the international community, as well as individual Venezuelans and institutions".
However, news agency AFX quoted an unnamed senior US official who drew a more direct link between the blasts and Mr Chavez's statement.
Mr Chavez "says these things and that is followed by this," he said, referring to the explosions.
Conversely, the Venezuelan Vice President, Jose Vicente Rangel, condemned "elements thinking of taking the route of terrorism" to oust Mr Chavez.
He told the BBC the Venezuelan Government would to anything in its power to avoid further acts of what he also termed "macro-terrorism".