What size of the fuses does fluke multimeters use?
If you replace the fuse with another type (particularly a smaller type) you will compromise the protection. The fuses used in multimeters are larger because they are rated to safely break relatively high voltages and high fault currents without excessive arcing and without exploding. Some meters from your supplier (you didn't give a model number) are rated at 600V 10A. If you are in the US, Home Despot lists them for $7 ea. Here is data from the Chinese manufacturer with links to UL and TUV certificates. SIBA brand also seems to be popular. Note the interrupting capacity of 10kA! At 600VDC! AGC10A fuses have an interrupting capacity of only 200A at only 250VAC (no DC rating).
If you never work with anything over a few volts this won't matter much (you might wreck your meter or burn yourself on the leads), but for mains voltages it is far more important and can definitely be a safety issue. If you are doing industrial electrician work, it  is mandatory, in my opinion, to have a meter with a Fluke level of protection. The consequences of arc flash in situations where fault currents can exceed 10kA are very unpleasant.
Fluke meters tend to have genuine  CAT III 600 V ratings and massive internal fuses to protect the user. For example, 11 A, 1000 V FAST Fuse (Fluke PN 803293) which costs about $10 in one-off. The meter you have uses a less protective fuse type, but still WAY better than a cheap ABC fuse.