From the agents point of view, he just wants a sale. If his fees are 2% (say) then he'll get an extra £60, so its just not worth it for the agent to jeopardise the sale for the sake of £60.
The person who is jeopardising the sale is the seller, but if the seller had a better offer then he'd get the agent to say (very nicely) that unless you raise your offer, then he'll have to do right by his family etc and accept the other offer. Either that or he'd accept that he has a moral obligation to stick with the deal he has made with you. (It all depends on what type of person the seller is).
But the agent is not saying that you must raise your offer or lose the house, he's asking you if there is any chance that you'll raise your offer whilst being careful not to back the seller into a corner where he'd lose the chance to sell the house to you.
So, if you raise your offer, don't do it because you imagine a bidding war, do it because you think you've worked out what point the seller will agree to sell to you.
Are the sellers a couple? You may find that one of them is in favour of going ahead with the price they agreed with you already and the other thinks they can do better. Just a bit of prejudice here, but if what's really going on is that the seller who wants more money really wants it because they think that the house is worth more than the neighbours, then it will be the half of the couple who was responsible for making the house look nice.
As an agent, there is nothing riskier than letting the two halves of a deal get to know each other because chances are one of them will say something really obnoxious to the other and scupper the deal. However, if you have met the sellers, you may be able to work out which of them is behind the request for more money and whether they'll be able to get their husband/ wife to agree to pull out of the deal if you don't help them out.
Of all the houses I ever visited, I never went into one that had been done up, that the person who had done it up didn't think it was the most beautiful in the road and therefore worth more than all the neighbours houses. Similarly, for the ones that needed a lot of work, the sellers were always convinced that it needed a lot less money spent on it than the buyers thought it would.