Juan Manuel Santos has been sworn in as the new president of Colombia.In his inaugural speech, Mr Santos said that mending relations with neighbours Ecuador and Venezuela would be one of his government's main priorities.
In response, Venezuelan President Hugo Chavez said he would like to meet "face-to-face" with Mr Santos.
Mr Santos also told Colombia's left-wing rebel groups the door to dialogue was open, but they would have to renounce violence first.
'New dawn'
He promised to tackle the main problems besetting Colombians, saying his government would aim to lower unemployment to a single digit figure, fight corruption and reduce poverty.
He said the work of his predecessor in office, President Alvaro Uribe, had paved the way for "a new dawn for Colombia".
Mr Santos, who served as Mr Uribe's defence minister, said the former president had inspired hope in Colombians and allowed them to move freely in their own country again.
He said it was now time the country moved from Mr Uribe's policy of "democratic security" to one of "democratic prosperity".
He asked the heads of the security forces to continue delivering results in their battle against left-wing rebels and drug traffickers.
But he made it clear to the rebels, who have been fighting a 46-year insurgency against the Colombian state, that he did not rule out dialogue completely.
"To the armed illegal groups, who invoke political reasons and now talk of dialogue and negotiation, I say my government is open to any kind of conversation which seeks to eradicate violence and build a more prosperous, equal and just society," he said.
He added that a dialogue would only go ahead if the rebels laid down their arms and stopped their campaign of kidnapping, intimidation, extortion and drug-dealing.
'Rebuilding trust'
On foreign policy, he tried to mend some of the relations which broke down during his predecessor's tenure.
In a reference to accusations by Venezuela's President Chavez that Mr Uribe had been planning an attack on Venezuela, President Santos said that the word "war" was not in his dictionary when he thought of Colombia's relations with its neighbours.
Mr Chavez broke off diplomatic ties with Colombia two weeks ago after Bogota accused him of harbouring Farc rebels.
The Venezuelan president did not attend the inauguration, but did send his Foreign Minister, Nicolas Maduro.
Speaking on live TV after Mr Santos' inauguration, Mr Chavez said he wanted to "turn over the page" in relations with Colombia.
He would be seeking a "face-to-face" meeting with Mr Santos.
The new Colombian president also appealed to Ecuador, whose president, Rafael Correa, was in the audience.
Ecuador cut its ties with Bogota after the Colombian military conducted a cross-border bombing raid on a Farc camp on Ecuadorian territory.
He said that one of his main priorities would be to rebuild trust between Colombia and its neighbours.
"Every country in our region has great strength, but together we can be a formidable power," he added.
