The party's Conor Murphy said the DUP has not met Sinn Féin during the talks process to discuss outstanding issues.
Mr Murphy also said the government is playing "footsie" with unionist parties.
A DUP spokesman dismissed Sinn Féin's claims that the party is not engaged in the talks process.
On Thursday, Sinn Féin held talks with the British and Irish governments, whose delegation was led by the Irish Foreign Minister Charlie Flanagan.
Speaking after the meeting, Mr Murphy said the talks process did not have a firm agenda or timetable.
The Newry and Armagh MP said: "Everyone needs to be in the talks process on the same basis", and added there had been no progress on reaching a "credible process of dialogue".
Talks began last week to examine a series of outstanding issues including the past, flags, parading, welfare reform, the workings of Stormont and budgetary matters.
Irish Foreign Minister Charlie Flanagan said he hoped he would be able to arrange talks with the DUP "in the not-too-distant future".
The Ulster Unionist Party (UUP) held talks with Mr Flanagan in Belfast on Thursday, led by the party's leader Mike Nesbitt, and the SDLP and Alliance party also took part in discussions about legacy issues.
Alliance leader David Ford said the parties "must get real" about their involvement in the talks, and called for an end to political "grandstanding".
The SDLP's Mark Durkan accused the DUP of having a "stand-back, hold-off attitude" to the talks, and said he hoped the presence of US envoy Gary Hart would bring "more pace" to the process.
The DUP stayed away from last week's opening session of the inter-party talks because it objected to negotiating with the Irish government about Northern Ireland's internal affairs.
On Wednesday, the party met the Secretary of State Theresa Villiers, but so far has not taken part in round-table talks.
A party spokesperson denied Sinn Féin's claims that the DUP was holding the talks process to "ransom", and said the First Minister Peter Robinson and Deputy First Minister Martin McGuinness held a 45-minute discussion on Wednesday in Cardiff.
He added that the DUP is also expected to hold further talks on Thursday evening with Ms Villiers.
Sinn Féin has said the Democratic Unionist Party (DUP) is holding the talks process to "ransom" over the parading dispute in north Belfast.