Northern Ireland's deputy first minister is in France as part of a two-day trip to World War One battlefields.
On Wednesday, he was in Flanders at the site of the Battle of Messines, where he laid a wreath.
Mr McGuinness said he "could never have envisaged that I would've been [at the Somme] as deputy first minister and a proud Irish republican".
His visit to the Somme was an attempt to recognise soldiers from Ireland who died in the battle and its importance to unionists, he said.
The battle of the Somme began on 1 July 1916 and lasted four-and-a-half months.
More than 3,500 soldiers from the 36th (Ulster) and 16th (Irish) divisions were killed and thousands more were injured.
"My duty is to represent everybody and I think it is very important that we all step out of our comfort zones and that we do recognise that reconciliation is the next important phase of the peace process," Mr McGuinness said.
"I do that knowing that there will be some people who are not in favour of that."
Sinn Féin's Martin McGuinness has laid a wreath at the site of the Battle of the Somme on Thursday.